calculus problems

dx and dy are called the differentials of x and y respectivel..

Let y = f (x) = x 1 / 4 Let x = 81, d x =1. Taking these values we have ..

a) Symmetry about x - axis If the equation of the curve remains unaltered when y is replaced by -y, then the curve is symmetrical about x-axis. b) Symmetry about y-axis If the equation of the curve remains unaltered when x is replaced by -x then the curve is symmetrical about y-axis. c) Symmetry a..

Symmetry (a) By replacing y by -y, the equation (1) is altered, therefore the curve is not symmetrical about x-axis. (b) By replacing x by -x, the equation of the curve is altered, therefore the curve is not symmetrical about y-axis. (c) Replace x and y by -x and -y respectively in the equation y ..

The points of intersection with x-axis is determined by letting y = 0. Putting y = 0, - sin 2x = 0 This implies the curve intersects the x-axis at the points where The points at which the tangent is parallel to x-axes are determined by solving. y = - sin 2x The tangent is paral..

This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. Let f be a function defined on an interval I and let x 1 and x 2 be any two points on I. (i) f is said to be increasing in the interval ..

(1) Let the given function be f (x) on the real number line R. (2) Differentiate the function f(x) with respect to x and equate it to zero i.e., put f '(x) = 0. Solve for x. These values of x which satisfy f '(x) = 0 are called Critical values of the function (3) Arrange these Critical values in a..

Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b)...

The value of c obtained need not be uniqu..