hard calculus problems

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieve..

Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined by th..

Let f(x) be a continuous function defined on an interval [a,b]. between the limits a and b. This statement is also known as 'fundamental theorem of calculus'. We call b, the upper limit of x and a, the lower limit. If in place of F(x) we take F(x)+c as the value of the integral, we have =..

Because of these condition, the 2 n d order differential equation y''= 2 has particular solution x 2 + x + 2. The values f (0) = 2 and f '(0) = 1 are called initial values. The problem of finding the solution of a differential equation that satisfies these prescribed initial conditions is..

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Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a heavy meteorite e..

Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the velocity of a he..

After having studied functions, limits and continuity in the previous chapter, we shall further divide the class of continuous functions into two sub classes, derivable and non-derivable.After having studied functions, limits and continuity in the previous chapter, we shall further divide the class..

First Fundamental Theorem of Integral Calculus Let f(x) be a continuous function on the closed interval [a, b]. Let the area function A(x) be defined ..

In this chapter, we have studied various techniques of differentiation. Also, we have studied the method of obtaining higher order derivatives of functions which is useful in maxima and minima problems.In this chapter, we have studied various techniques of differentiation. Also, we have s..