calculus motion problems

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..

Differential calculus can be considered as mathematics of motion, growth and change where there is a motion, growth, change. Whenever there is variable forces producing acceleration, differential calculus is the right mathematics to appl..

If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..

If f (x) is a function continuous on [a, b] then Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(b) ..

The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Calculus. The differentiation of functions are widely used in science, economics, medicine and computer scienc..

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..