How to find derivative of a parametric function?

When a particle moves on the plane,it can be described uncounted points corresponding to coordinates in a Cartesian coordinate system with the same unit on the each axis.However,not all the processes are convenient to express y in terms x.At times a relationship between x and y in terms of a third variable which is a various time t,is mexessary.     

How to find derivative of a parametric function?(2)

Example 2:At time t≥0,aparticle moving in the xy-plane has vector given by V(t)=[X(t),Y(t)]=[t2,5t].What is the acceleration vector of the particle at timet=3? Solution:From the condition is given,we know X(t)=t2 and Y(t)=5t.     

What is a polar function and how to find derivative of it?

1. What are polar coordinates? I went from Chongqing to Beijing by air in 1992. When I came to the airport and watched big jetliners lumber into position on the runway for takeoff at the first time in my life, I asked questions to partner about how big jetliners got off at that position exactly. He made sure that people     

How does the Chain Rule work？ （2）

Example 2 ： If f（x） =√5-3x,find f′（x）.
SOLUTION：
Setu=5-3x,then f（x）=y=u^1/2.     

转换角度

解题时,如果仅根据题面的信息,往往会陷入“山重水复疑无路”的境地,淹没在计算的海洋之中,即便求解出来,仍感觉索然无味;反之,转换角度、合理转化,顿觉“柳暗花明”,豁然开朗,回首赏析,会有“一览众山小”之感,兴味盎然．     

数列单调性的一种判断

一个数列,判断其单调性,常常十分有用．要判断{xn}单调,常用的方法是证明在n=1,2,…,xn＋1-xn有确定的符号．但有时,     

How to use the method of the improvising differentiation？

We know the Substitution Rule, which is based on the following identity in differentiation.∫f（g（x））g＇（x）dx=∫（u）du（where u= g（x）） . Now, we＇ll talk about how to use the method of the improvising differentiation, and give some examples by using basic integration formulas, such as,∫（1/x）dx=1n｜x｜＋C called the Log Rule for integration,∫e^x dx=e^x＋C called the Exponential Rule.     

巧解一题

题目（2005年全国理科）（1）设函数f（x）=xlog2x＋（1-x）log2（1-x）（0〈x〈1）,求,（x）的最小值;（2）设正数p1,p2,p3,…,p2^n满足p1＋p2＋p3＋…＋p2^n=1,求证：p1log2p1＋p2log2p2＋p3log2p3＋…＋p2^nlog2p2^n≥-n．     

How to find the area between two functions?

High School Attached CNU(1 00048) Yuxue Liang Last time we have done Example 1,there is not only one function in fact,b ecause x-axis is the function y=0.Example 1:Find the area between     

The complex step approximation to the Fréchet derivative of a matrix function

We show that the Fréchet derivative of a matrix function f at A in the direction E, where A and E are real matrices, can be approximated by Im f(A + ihE)/h for some suitably small h. This approximation, requiring a single function evaluation at a complex argument, generalizes the complex step approximation known in the scalar case. The approximation is proved to be of second order in h for analytic functions f and also for the matrix sign function. It is shown that it does not suffer the inherent cancellation that limits the accuracy of finite difference approximations in floating point arithmetic. However, cancellation does nevertheless vitiate the approximation when the underlying method for evaluating f employs complex arithmetic. The ease of implementation of the approximation, and its superiority over finite differences, make it attractive when specialized methods for evaluating the Fréchet derivative are not available, and in particular for condition number estimation when used in conjunction with a block 1-norm estimation algorithm.     

What is The Mean Value Theorem？ （2）

2. How does the MVT work？Examplel： Iff（x） = x^2,F（x） = x^3 ,Find ξ on the interval [0, 1] using MVT.