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  • SQL SERVER – What is Page Life Expectancy (PLE) Counter

    - by pinaldave
    During performance tuning consultation there are plenty of counters and values, I often come across. Today we will quickly talk about Page Life Expectancy counter, which is commonly known as PLE as well. You can find the value of the PLE by running following query. SELECT [object_name], [counter_name], [cntr_value] FROM sys.dm_os_performance_counters WHERE [object_name] LIKE '%Manager%' AND [counter_name] = 'Page life expectancy' The recommended value of the PLE counter is 300 seconds. I have seen on busy system this value to be as low as even 45 seconds and on unused system as high as 1250 seconds. Page Life Expectancy is number of seconds a page will stay in the buffer pool without references. In simple words, if your page stays longer in the buffer pool (area of the memory cache) your PLE is higher, leading to higher performance as every time request comes there are chances it may find its data in the cache itself instead of going to hard drive to read the data. Now check your system and post back what is this counter value for you during various time of the day. Is this counter any way relates to performance issues for your system? Note: There are various other counters which are important to discuss during the performance tuning and this counter is not everything. Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, SQLServer, T SQL, Technology

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  • SQL SERVER – Find Most Expensive Queries Using DMV

    - by pinaldave
    The title of this post is what I can express here for this quick blog post. I was asked in recent query tuning consultation project, if I can share my script which I use to figure out which is the most expensive queries are running on SQL Server. This script is very basic and very simple, there are many different versions are available online. This basic script does do the job which I expect to do – find out the most expensive queries on SQL Server Box. SELECT TOP 10 SUBSTRING(qt.TEXT, (qs.statement_start_offset/2)+1, ((CASE qs.statement_end_offset WHEN -1 THEN DATALENGTH(qt.TEXT) ELSE qs.statement_end_offset END - qs.statement_start_offset)/2)+1), qs.execution_count, qs.total_logical_reads, qs.last_logical_reads, qs.total_logical_writes, qs.last_logical_writes, qs.total_worker_time, qs.last_worker_time, qs.total_elapsed_time/1000000 total_elapsed_time_in_S, qs.last_elapsed_time/1000000 last_elapsed_time_in_S, qs.last_execution_time, qp.query_plan FROM sys.dm_exec_query_stats qs CROSS APPLY sys.dm_exec_sql_text(qs.sql_handle) qt CROSS APPLY sys.dm_exec_query_plan(qs.plan_handle) qp ORDER BY qs.total_logical_reads DESC -- logical reads -- ORDER BY qs.total_logical_writes DESC -- logical writes -- ORDER BY qs.total_worker_time DESC -- CPU time You can change the ORDER BY clause to order this table with different parameters. I invite my reader to share their scripts. Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, SQLAuthority News, SQLServer, T SQL, Technology Tagged: SQL DMV

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  • SQLAuthority News – 18 Seconds of Fame – My PASS Experience

    - by pinaldave
    Happy Holidays to All of YOU! Life is full of little and happy surprises. I think Christmas and Santa are based on it. I just received very interesting email earlier today, I had no idea about it. Earlier this year, I had visited Seattle to attend SQLPASS – read the complete summary over here: SQLAuthority News – SQLPASS Nov 8-11, 2010-Seattle – An Alternative Look at Experience. While I was walking down, someone has stopped me and asked if they can talk to me for 15 seconds, I said yes and they had shot quick movie with mobile. The conversation was very quick and I had forgotten about it. Today I received email from one of the blog reader about it being on YouTube. Honestly, I did not know if this was ever going to be on YouTube. I am surprised and thrilled. Watch my 18 seconds fame movie. Reference: Pinal Dave (http://blog.sqlauthority.com) Filed under: About Me, Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Server, SQL Tips and Tricks, SQLAuthority Author Visit, T SQL, Technology

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  • SQL SERVER – Plan Cache and Data Cache in Memory

    - by pinaldave
    I get following question almost all the time when I go for consultations or training. I often end up providing the scripts to my clients and attendees. Instead of writing new blog post, today in this single blog post, I am going to cover both the script and going to link to original blog posts where I have mentioned about this blog post. Plan Cache in Memory USE AdventureWorks GO SELECT [text], cp.size_in_bytes, plan_handle FROM sys.dm_exec_cached_plans AS cp CROSS APPLY sys.dm_exec_sql_text(plan_handle) WHERE cp.cacheobjtype = N'Compiled Plan' ORDER BY cp.size_in_bytes DESC GO Further explanation of this script is over here: SQL SERVER – Plan Cache – Retrieve and Remove – A Simple Script Data Cache in Memory USE AdventureWorks GO SELECT COUNT(*) AS cached_pages_count, name AS BaseTableName, IndexName, IndexTypeDesc FROM sys.dm_os_buffer_descriptors AS bd INNER JOIN ( SELECT s_obj.name, s_obj.index_id, s_obj.allocation_unit_id, s_obj.OBJECT_ID, i.name IndexName, i.type_desc IndexTypeDesc FROM ( SELECT OBJECT_NAME(OBJECT_ID) AS name, index_id ,allocation_unit_id, OBJECT_ID FROM sys.allocation_units AS au INNER JOIN sys.partitions AS p ON au.container_id = p.hobt_id AND (au.TYPE = 1 OR au.TYPE = 3) UNION ALL SELECT OBJECT_NAME(OBJECT_ID) AS name, index_id, allocation_unit_id, OBJECT_ID FROM sys.allocation_units AS au INNER JOIN sys.partitions AS p ON au.container_id = p.partition_id AND au.TYPE = 2 ) AS s_obj LEFT JOIN sys.indexes i ON i.index_id = s_obj.index_id AND i.OBJECT_ID = s_obj.OBJECT_ID ) AS obj ON bd.allocation_unit_id = obj.allocation_unit_id WHERE database_id = DB_ID() GROUP BY name, index_id, IndexName, IndexTypeDesc ORDER BY cached_pages_count DESC; GO Further explanation of this script is over here: SQL SERVER – Get Query Plan Along with Query Text and Execution Count Reference: Pinal Dave (http://blog.SQLAuthority.com) Filed under: Pinal Dave, SQL, SQL Authority, SQL Optimization, SQL Performance, SQL Query, SQL Scripts, SQL Server, SQL Tips and Tricks, T SQL Tagged: SQL Memory

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  • algorithm for Virtual Machine(VM) Consolidation in Cloud

    - by devansh dalal
    PROBLEM: We have N physical machines(PMs) each with ram Ri, cpu Ci and a set of currently scheduled VMs each with ram requirement ri and ci respectively Moving(Migrating) any VM from one PM to other has a cost associated which depends on its ram ri. A PM with no VMs is shut down to save power. Our target is to minimize the weighted sum of (N,migration cost) by migrating some VMs i.e. minimize the number of working PMs as well as not to degrade the service level due to excessive migrations. My Approach: Brute Force approach is choosing the minimum loaded PM and try to fit its VMs to other PMs by First Fit Decreasing algorithm or we can select the victim PMs and target PMs based on their loading level and shut down victims if possible by moving their VMs to targets. I tried this Greedy approach on the Data of Baadal(IIT-D cloud) but It isn't giving promising results. I have also tried to study the Ant colony optimization for dynamic VM consolidating but was unable to understand very much. I used the links. http://dumas.ccsd.cnrs.fr/docs/00/72/52/15/PDF/Esnault.pdf http://hal.archives-ouvertes.fr/docs/00/72/38/56/PDF/RR-8032.pdf Would anyone please explain the solution or suggest any new approach for better performance soon. Thanks in advance.

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  • How to optimize a box2d simulation in action game?

    - by nathan
    I'm working on an action game and i use box2d for physics. The game use a tiled map. I have different types of body: Static ones used for tiles Dynamic ones for player and enemies Actually i tested my game with ~150 bodies and i have a 60fps constantly on my computer but not on my mobile (android). The FPS drop as the number of body increase. After having profiled the android application, i saw that the World.step took around 8ms in CPU time to execute. Here are few things to note: Not all the world is visible on screen, i use a scrolling system Enemies are constantly moving toward the player so there is alaways to force applied to their body Enemies need to collide between each others Enemies collide with tiles I also now that i can active/desactive or sleep/awake bodies. Considering the fact that only a part of the enemies are possibly displayed on screen, is there any optimizations i can do to reduce the execution time of box2d simulation? I found a guy trying an optimization based on distance of enemies from the player (link). But i seems like he just desactives far bodies (in my case, i could desactive bodies that are not visible). But my enemies need to move even when they are not visible on screen, and applying forces will not workd on inactive bodies. Should i play with sleeping bodies here? Also, enemies are composed by two fixtures and are constantly colliding with each others and with tiles but i really never need to get notified about that. Is there anything i can do to optimize this kind of scenario? Finally, am i wrong to try to run simulation at 60FPS on mobile and should i try to make it run at 30FPS?

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  • Efficient algorithm for Virtual Machine(VM) Consolidation in Cloud

    - by devansh dalal
    PROBLEM: We have N physical machines(PMs) each with ram Ri, cpu Ci and a set of currently scheduled VMs each with ram requirement ri and ci respectively Moving(Migrating) any VM from one PM to other has a cost associated which depends on its ram ri. A PM with no VMs is shut down to save power. Our target is to minimize the weighted sum of (N,migration cost) by migrating some VMs i.e. minimize the number of working PMs as well as not to degrade the service level due to excessive migrations. My Approach: Brute Force approach is choosing the minimum loaded PM and try to fit its VMs to other PMs by First Fit Decreasing algorithm or we can select the victim PMs and target PMs based on their loading level and shut down victims if possible by moving their VMs to targets. I tried this Greedy approach on the Data of Baadal(IIT-D cloud) but It isn't giving promising results. I have also tried to study the Ant colony optimization for dynamic VM consolidating but was unable to understand very much. I used the links. http://dumas.ccsd.cnrs.fr/docs/00/72/52/15/PDF/Esnault.pdf http://hal.archives-ouvertes.fr/docs/00/72/38/56/PDF/RR-8032.pdf Would anyone please clarify the solution or suggest any new approach/resources for better performance. I am basically searching for the algorithms not the physical optimizations and I also know that many commercial organizations have provided these solution but I just wanted to know more the underlying algorithms. Thanks in advance.

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  • AndroMDA maven code generation and JPA Annotations

    - by ArsenioM
    I am using the AndroMDA plugin for maven to generate code from an uml diagram made in MagicDraw. When the code is generated, AndroMDA desings the JPA annotation for the persitence layer. I think that at the compilation process AndroMDA uses Naming Strategies to determine the Table and Column names for the DataBase. I want to determine how AndroMDA desings this JPA annotations, because I need to display this DataBase names based on the UML entity and atributtes names. I was regarding if there is an API of AndroMDA that I could use to do this by giving it the uml diagram. Or at least, to know the Naming Strategies used by AndroMDA to achive that. AndroMDA at the compilation process design the JPA annotations for the Entities, Attributes, etc that are written in my java classes under a series of rules that exist within the EJB3 cartridge of AndroMDA. (The further Database is created using those JPA annotations). I want to create a program that returns me the same Table and Attributes names wrote on the JPA annotations, by giving it the .xml file of the uml diagram of a project. I was hoping that I could take advantage of the EJB3 cartridge to generate those Tables and Attribute names with my program. One way could be using an API of AndroMDA that do this(if it exits), or at least, by implementing the same rules used by the EJB3 cartridge for that matter. To be more illustrative, For example: If in my uml model I have an Entity called “CompanyGroup”, AndroMDA would generate the following code for the class definition: @javax.persistence.Entity @javax.persistence.Table(name = "COMPANY_GR") Public class CompanyGroup implements java.io.Serializable, Comparable< CompanyGroup This is just an example (not a real case), but nevertheless, the way how AndroMDA do the translation from “CompanyGroup” to “COMPANY_GR” has to be specified somewhere. Hope this explanation is useful enough. Thanks.

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  • Code Golf: Easter Spiral

    - by friol
    What's more appropriate than a Spiral for Easter Code Golf sessions? Well, I guess almost anything. The Challenge The shortest code by character count to display a nice ASCII Spiral made of asterisks ('*'). Input is a single number, R, that will be the x-size of the Spiral. The other dimension (y) is always R-2. The program can assume R to be always odd and = 5. Some examples: Input 7 Output ******* * * * *** * * * * ***** * Input 9 Output ********* * * * ***** * * * * * * *** * * * * * ******* * Input 11 Output *********** * * * ******* * * * * * * * *** * * * * * * * * ***** * * * * * ********* * Code count includes input/output (i.e., full program). Any language is permitted. My easily beatable 303 chars long Python example: import sys; d=int(sys.argv[1]); a=[d*[' '] for i in range(d-2)]; r=[0,-1,0,1]; x=d-1;y=x-2;z=0;pz=d-2;v=2; while d>2: while v>0: while pz>0: a[y][x]='*'; pz-=1; if pz>0: x+=r[z]; y+=r[(z+1)%4]; z=(z+1)%4; pz=d; v-=1; v=2;d-=2;pz=d; for w in a: print ''.join(w); Now, enter the Spiral...

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  • how to push a string address to stack with assembly, machine code

    - by Yigit
    Hi all, I am changing minesweeper.exe in order to have an understanding of how code injection works. Simply, I want the minesweeper to show a message box before starting. So, I find a "cave" in the executable and then define the string to show in messagebox and call the messagebox. Additionally of course, I have to change the value at module entry point of the executable and first direct it to my additional code, then continue its own code. So at the cave what I do; "hello starbuck",0 push 0 //arg4 of MessageBoxW function push the address of my string //arg3, must be title push the address of my string //arg2, must be the message push 0 //arg1 call MessageBoxW ... Now since the memory addresses of codes in the executable change everytime it is loaded in the memory, for calling the MessageBoxW function, I give the offset of the address where MessageBoxW is defined in Import Address Table. For instance, if MessageBoxW is defined at address1 in the IAT and the instruction just after call MessageBoxW is at address2 instead of writing call MessageBoxW, I write call address2 - address1. So my question is, how do I do it for pushing the string's address to the stack? For example, if I do these changes via ollydbg, I give the immediate address of "hello starbuck" for pushing and it works. But after reloading the executable or starting it outside of ollydbg, it naturally fails, since the immediate addresses change. Thanks in advance, Yigit.

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  • TypeScript - separating code output

    - by Andrea Baccega
    i'm trying typescript and I find it very useful. I've a quite large project and i was considering rewriting it using typescript. The main problem here is the following: file A.ts: class A extends B { // A stuff } file B.ts: class B { // B stuff } If I compile A.ts with this command: tsc --out compiledA.js A.ts I'll get error from the compiler cause he doesn't know how to threat the "B" after extends. So, a "solution" would be including in A.ts (as first line of code): /// <reference path="./B.ts" /> Compiling again A.ts with the same command tsc --out compiledA.js A.ts Will result in compiledA.js containing both B.ts and A.ts code. ( which could be very nice ) In my case, I only need to compile the A.ts code in the compiledA.js file and I don't want the B.ts stuff to be in there. Indeed, what I want is: tsc --out A.js A.ts = compile only the A.ts stuff tsc --out B.js B.ts = compile only the B.ts stuff I can do it by removing the "extends" keyword but doing that I'll loose most of the typescript goodness. Can someone telll me if there's a way to do this ?

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  • NetBeans parameter fill after code completion

    - by byte
    This is a particularly annoying problem I'm having, and I can't be the only one to have issue with it. In NetBeans, when you type part of a method, then hit CTRL-SPACE, it displays the code-completion popup, whereupon you can hit tab to finish out the word. This is great, and pretty much how all IDE's operate. Example: Thread.sl < CTRL-SPACE Thread.sleep Yay! Problem is that in this context, once you type in a paren, it auto-fills the parameters for the method with their default names, and inserts a closing paren (regardless of whether you have disabled the option to automatically close them on the preferences page for code completion). This behavior is NOT present if you had manually typed out the full name. How is this helpful to anyone? You've got to type over it your actual variable that you will be passing, and NetBeans gives you no option to prevent the closing paren on code-completion. Does anyone have a way to solve this issue, without having to dive into the netbeans source and build it just for this minor of an issue?

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  • How can I run an app's source code that I got from the Android source code?

    - by Wesley
    For all of you android devs out there that have the Android simulator running on your comp, you know that there are a few built in apps that are already 'installed' on your phone. I had an idea for an app that would utilize a function that is already being done in the spare parts app. I went on to the android developer site, dug through the source code files, and found the spare parts app, and am now trying to set it up so that running it from eclipse on my machine actually runs the app in the simulator. In other words, I want to be able to make changes to and adjust some of the things in that app for my own needs. But it won't compile, because of a number of different errors. How do I get that source code running on my local machine? Is there some special trick that I just dont know about? I thought that if I could get the source code than the rest would be easy, but it isn't being too easy. Any help here would be appreciated!!

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  • Linq to SQL code generator features

    - by Anders Abel
    I'm very fond of Linq to SQL and the programming model it encourages. I think that in many cases when you are in control of both the database schema and the code it is not worth the effort to have different relational and object models for the data. Working with Linq to SQL makes it simple to have type safe data access from .NET, using the partial extension methods to implement business rules. Unfortunately I do not like the dbml designer due to the lack of a schema refresh function. So far I have used SqlMetal, but that lacks the customization options of the dbml designer. Because of that I've started working on a tool which regenerates the whole code file like SqlMetal, but has the ability to do the customizations that are available in the dbml designer (and maybe more in the future). The customizations will be described in an xml file which only contains those parts that shouldn't have default values. This should keep the xml file size down as well as the maintenance burden of it. To help me focus on the right features, I would like to know: What would be your favourite feature in a linq to sql code generator?

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  • Code Coverage tool for BlackBerry

    - by Skrud
    I'm looking for a code coverage tool that I can use with a BlackBerry application. I'm using J2ME-Unit for Unit Testing and I want to see how much of my code is being covered by my tests. I've tried using Cobertura for J2ME but after days of wrestling with it I failed to get any results from it. (I believe that the instrumentation is un-done by the RAPC compilation). And despite this message, the project seems to be dead. I've looked at JInjector but the project seems very incomplete. There is little (if any) documentation and although it claims to be able to work with BlackBerry projects, I haven't seen any places where it has been used for that purpose. I've played with the project quite a bit but to no avail. I've also tried the "Coverage" view in the BlackBerry JDE, even though I use Eclipse for development. The view stays permanently blank, regardless of clicking "Refresh" and running the application from the JDE. I've looked at most of the tools on this SO thread, but they won't work with J2ME/BlackBerry projects. Has anyone had any success with any code coverage tools on the BlackBerry? If so, what tools have you used? How have you used them? If anyone has managed to get JInjector or Cobertura for J2ME to work with a BlackBerry project, what did you have to do to get it working?

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  • Problem writing a snippet containing Emacs Lisp code

    - by user388346
    Hi all, I've been trying to make use of a cool feature of YASnippet: write snippets containing embedded Emacs Lisp code. There is a snippet for rst-mode that surrounds the entered text with "=" that is as long as the text such as in ==== Text ==== Based on this snippet, I decided to slightly modify it (with Elisp) so that it comments out these three lines depending on the major mode you are in (I thought that such a snippet would be useful to organize the source code). So I wrote this: ${1:`(insert comment-start)`} ${2:$(make-string (string-width text) ?\-)} $1 ${2:Text} $1 ${2:$(make-string (string-width text) ?\-)} $0 This code works relatively well except for one problem: the indentation of these three lines gets mixed up, depending on the major mode I'm in (e.g., in emacs-lisp-mode, the second and the third lines move more to the right than the first line). I think the source of the problem might have something to do with what comes after the string ${1: on the first line. If I add a character, I have no problem (i.e., all three lines are correctly aligned at the end of the snippet expansion). If I add a single space after this string, the misalignment problem still continues though. So my question is: do you know of any way of rewriting this snippet so that this misalignment does not arise? Do you know what's the source of this behaviour? Cheers,

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  • How to Inject code in c# method calls from a separate app

    - by Fusspawn
    I was curious if anyone knew of a way of monitoring a .Net application's runtime info (what method is being called and such) and injecting extra code to be run on certain methods from a separate running process. say i have two applications: app1.exe that for simplicity's sake could be class Program { static void Main(string[] args) { while(true){ Somefunc(); } } static void Somefunc() { Console.WriteLine("Hello World"); } } and I have a second application that I wish to be able to detect when Somefunc() from application 1 is running and inject its own code, class Program { static void Main(string[] args) { while(true){ if(App1.SomeFuncIsCalled) InjectCode(); } } static void InjectCode() { App1.Console.WriteLine("Hello World Injected"); } } So The result would be Application one would show Hello World Hello World Injected I understand its not going to be this simple ( By a long shot ) but I have no idea if it's even possible and if it is where to even start. Any suggestions ? I've seen similar done in java, But never in c#. EDIT: To clarify, the usage of this would be to add a plugin system to a .Net based game that I do not have access to the source code of.

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  • What is the minimal licensable source code?

    - by Hernán Eche
    Let's suppose I want to "protect" this code about being used without attribution, patenting it, or through any open source licence... #include<stdio.h> int main (void) { int version=2; printf("\r\n.Hello world, ver:(%d).", version); return 0; } It's a little obvious or just a language definition example.. When a source stop being "trivial, banal, commonplace, obvious", and start to be something that you may claim "rights"? Perhaps it depends on who read it, something that could be great geniality for someone that have never programmed, could be just obvious for an expert. It's easy when watching two sources there are 10000 same lines of code, that's a theft.. but that's not always so obvious. How to measure amount of "ownness", it's about creativity? line numbers? complexity? I can't imagine objetive answers for that, only some patches. For example perhaps the complexity, It's not fair to replace "years of engeneering" with "copy and paste". But is there any objetive index for objetive determination of this subject? (In a funny way I imagine this criterion: If the licence is longer than the code, then there is no owner, just to punish not caring storage space and world resources =P)

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  • FREE eBook: .NET Performance Testing and Optimization (Part 1)

    In this this first part of complete guide to performance profiling, Paul Glavich and Chris Farrell explain why performance testing is a good idea and walk you through everything you need to know to set up a test environment. This comprehensive guide to getting started is an essential handbook to any programmer looking to set up a .NET testing environment and get the best results out of it. Download your free copy now span.fullpost {display:none;}

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  • Silverlight: Search Engine Optimization

    - by xamlnotes
    I am doing lots of consulting on Silverlight these days. So I was looking into search enabling Sl applications. So I found this great whitepaper on this very subject. I will post more on this same subject as I get into implementing these ideas as well as some of my own I want to try out. Silverlight is really rocking the world today with more and more applications rolling out. So check out this great whitepaper to see whats cooking with SEO for yours. http://www.silverlight.net/learn/whitepapers/seo-for-silverlight/

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  • Extreme Optimization – Curves (Function Mapping) Part 1

    - by JoshReuben
    Overview ·        a curve is a functional map relationship between two factors (i.e. a function - However, the word function is a reserved word). ·        You can use the EO API to create common types of functions, find zeroes and calculate derivatives - currently supports constants, lines, quadratic curves, polynomials and Chebyshev approximations. ·        A function basis is a set of functions that can be combined to form a particular class of functions.   The Curve class ·        the abstract base class from which all other curve classes are derived – it provides the following methods: ·        ValueAt(Double) - evaluates the curve at a specific point. ·        SlopeAt(Double) - evaluates the derivative ·        Integral(Double, Double) - evaluates the definite integral over a specified interval. ·        TangentAt(Double) - returns a Line curve that is the tangent to the curve at a specific point. ·        FindRoots() - attempts to find all the roots or zeroes of the curve. ·        A particular type of curve is defined by a Parameters property, of type ParameterCollection   The GeneralCurve class ·        defines a curve whose value and, optionally, derivative and integrals, are calculated using arbitrary methods. A general curve has no parameters. ·        Constructor params:  RealFunction delegates – 1 for the function, and optionally another 2 for the derivative and integral ·        If no derivative  or integral function is supplied, they are calculated via the NumericalDifferentiation  and AdaptiveIntegrator classes in the Extreme.Mathematics.Calculus namespace. // the function is 1/(1+x^2) private double f(double x) {     return 1 / (1 + x*x); }   // Its derivative is -2x/(1+x^2)^2 private double df(double x) {     double y = 1 + x*x;     return -2*x* / (y*y); }   // The integral of f is Arctan(x), which is available from the Math class. var c1 = new GeneralCurve (new RealFunction(f), new RealFunction(df), new RealFunction(System.Math.Atan)); // Find the tangent to this curve at x=1 (the Line class is derived from Curve) Line l1 = c1.TangentAt(1);

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