What is the differential equation？

An equation involving a derivative is called a differential equation.Such as,dy/dx=2x,and the function y=f（x）satisfies this equation.When we know the additional condition that y=2 when x=-1,the function y=f（x）will be find exactly.The additional condition is called the initial condition.It is used to evaluate constant of integration.     

What is the limit of an infinite sequence？

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What is The Squeeze （or Sandwich） Theorem？

Let＇s do an exercise as warming up.Ex：Find lim x→0sin1/x.lim x→0sin1/x=lim1/x→∞sin1/x=lim t→∞sint（Let t=1/x）.We know lim t→∞sint does not exist,so lim x→0sin1/x DNE.We can use graphing calculator to show the result is DNE（from figure 1to figure 8）.     

What is the Substitution Rule?

When I learned the following basic formula of indefinite integrals in the calculus,at that time I was a teenager,the strange ideas had jump out my head.I would be a great girl in math if I can change all the ? in the following formula to the real functions     

How does the Chain Rule work？ （1）

Do you remember the＇ composite function which is composed of two functions, we＇ve learned. Such as f（x） =g（φ（x）） with φ（x） is called inside function and g（x） is called outside function.     

What is the basic integration rule？

In this paper you will learn the basic integration rule from the basic differentiation rule.
Last time we have learned anti-derivative, indefinite integral, and the power rule in integration.     

What does Part 2 of the Fundamental Theorem of Calculus mean?

We defined the indefinite integral as an anti-derivative,and defined the definite integral as the limit of Riemann sums.Both of them are very different and seem to be little in common.Part 1of the Fundamental Theorem of Calculus shows how indefinite integration and definite integration are related.In the other words,it shows how anti-derivative and the area are related.Today,we’ll learn Part 2 of the Fundamental Theorem of Calculus.     

What is the differential equation？

An equation involving a derivative is called a differential equation. Such as,     

Approximation integration by using rectangles

In calculus,two famous problems are well known.The one problem of finding the tangent line led us to the derivative.The other problem of finding area led us to find the definite integral.In this paper,we will learn how to approximation integration by using rectangles.1.What does the Riemann sum mean？A given function y=f（x）is continuous on the interval[a,b].     

The definite integral

1. What does the definite integral mean？
The definite integral off（x） from a to b is defined the limit of the sum as n→∞.     

What is The Mean Value Theorem？ （1）

All the textbooks about calculus are shown the Rolle＇s theorem at the first, then the Mean Value Theorem （MVT）. In some persons＇ opinion, the Rollers theorem is the special case of the MVT.     

Average value of a function

How to find the mean or the average value of a finite numbers？     

The volume problem in calculus

Everyone knows that the area of the base of solid is A,and the height is h,then the volume of it is V=A·h.It＇s an experience on math class in primer or middle school.Although you have an intuitive idea of what volume means,however,you can make this idea precise by using calculus to give an exact definition of volume.You will know what the concept of volume is in the calculus.