calculus problems

From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration (iii) These theorems give an..

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...

Differentiation deals with the rate of change while integration deals with the total change. The definite integrals are evaluated in problems relating to plane, areas, areas and volumes of solid of revolution etc. In this chapter, we confine ourselves to properties of definite int..

We have already defined, for a continuous function f(x) on a closed interval [a, b] as the area of the region bounded by the curve y = f(x), X-axis and x= a and x = b. In other words, area of the shaded region is a function of x. The function A(x) is shown in figure below. This area function A(x) i..

According to the problem Integrating, we have y = x 2 c This is the family of equations with parameter. The family of curves is represented by y = x 2 c, since one of these curves passes through (3,- 4), we have 4x 2 +..

Introduction - During the course of study of Mathematics, we must have come across several parts of inverse operations like (addition, subtraction) (multiplication, division) (forming an equation whose roots are given - solving a given equation) and so on. In practical situations, we may be interes..

Let the initial population be P 0 and P be the population of the colony at any instant t. Then according to the problem when t = 0, P= P 0 Equation (1) becomes log P = kt + log P 0 .(2) when P 0 is doubled, P = 2P 0 where t = 50 days From equation (2) log (2 P 0 ) = 50 k + lo..

Let m 0 be the moisture content initially and let m be the moisture content after t hours. According to problem: when t = 0, m= m 0 log m = kt + log m 0 ..

In this chapter we have learnt the application of derivatives to rate measure, also we have used the geometrical measurement of to find the equations of the tangent and normal to a curve at any point on the curve, angle of intersection of the curves. The derivatives also help in examining the behav..

Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in measurement,..