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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 2.6 - Problem 88ae
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 2.6 - Problem 88ae

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# Ch 2.6 - 88AE

ISBN: 9780321570567 2

## Solution for problem 88AE Chapter 2.6

Calculus: Early Transcendentals | 1st Edition

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Problem 88AE

88AE

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Solution 88AE Step-1 A continuous function can be formally defined as a f unction f : x y ,where the preimage of every open set in y is open in x. More concretely, a function f(x) in a single variable x is said to be continuous at point x if, 0 1. If f(x 0 is defined, so that x 0 is in the domain of ‘ f’. 2. lim f(x) exists for x in the domain of f. x x0 3. lim f(x) = f( x ). x x0 0 Left continuous : lim f(x) = f(a) , then f(x) is called a left continuous at x=a. xa Right continuous : lim xa)+= f(a) , then f(x) is called a right continuous at x=a. If , lim f(x) = f(a) = lim f(x) , then f(x) is called a continuous function at x=a. xa xa+ If , f(x) is not continuous at x =a means , it is discontinuous at x=a. Step-2 For any real number x the absolute value or modulus of x is denoted by x . | | | |= { x , if x 0 = { -x , if x 0. The graph of x | |; f(x) = | | It makes a right angle at (0,0) It is an even function. Its domain is the real numbers R, and its range is the non -negative real numbers : [ 0 , +). Step-3 The given function is f(x) = |x2| , at x=2. x2 |x2| Left hand limit : lim f(x) lim x2 x2 x2 (x2) = (x2) , since x | 2 = |(x-2) ,if x 2. = -1. Therefore, lim f(x) = -1. x2 Right hand limit : lim f(x) = lim |2| x2+ x2+ x2 = (x2), since x 2 = (x-2) ,if x 2 (x2) | | = 1. Therefore, lim f(x) = 1. + x2 Hence , lim f(x) = -1 = / 1 = lim f(x) x2 x2 + Therefore , f(x) is not continuous at x =2. Here , lim f(x) and lim f(x) both exists and are not equal to then we say that f has a jump + x2 x2 discontinuity at x=2. NOTE ; Jump discontinuity; It is caused when the function jumps from one point to another in its graph.

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##### ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: . This expansive textbook survival guide covers 112 chapters, and 7700 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “88AE” is broken down into a number of easy to follow steps, and 1 words. The full step-by-step solution to problem: 88AE from chapter: 2.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 88AE from 2.6 chapter was answered, more than 432 students have viewed the full step-by-step answer.

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