functions intervals

We can take the value of f at a (i.e., f(a)) as first estimate for average value of the function. Divide [a, b] into two equal parts such that then the second estimate of the average value of the function can be taken as second estimate of the average value of the functionh..

A function f(x) is said to be continuous in an interval I, if it is continuous at each point of I. then x can approach c both from the left and the right and so for f (x) to be continuous at c, we must have If the interval I is the closed interval [a,b], then..

Find the range of the function in interval notation. y = - x 2 + 2 => (- ∞, 2] or [- 2, ∞) or (- ∞, 2) or [2, ∞) or (- ∞, - 2]..

Periodic Functions - The trigonometric functions belong to a large class of functions called periodic functions in which there is a regular repetition of the values of the function over a certain interval..

A function is said to be monotonic if it is either increasing or decreasing but not both in a given interval. Consider the function The given function is increasing function on R. Therefore it is a monotonic function in [0,1]. It has it..

Find the interval on which the function y = ( x - 5) 2 is increasing. => [5, ∞) or [5, ∞] or [- 5, 5) or (5, ∞]..

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..

Use Newton's method to find the zero of the function in the interval [- 1, 0] to the nearest four decimal places. f ( x ) = ln (2 + x ) + x => - 0.4428 or - 0.4621 or - 0.3 or - 1.386 or - 0.5..

Increasing and Decreasing Functions - 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 b..

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 I, ..