   Chapter 1.8, Problem 19E

Chapter
Section
Textbook Problem

Explain why the function is discontinuous at the given number a. Sketch the graph of the function. f ( x ) = { 1 − x 2 if x < 1 1 / x if x ≥ 1                   a = 1

To determine

To discuss: Discontinuity of function at point a = 1 and sketch the graph.

Explanation

1) Concept:

As given function is piecewise continuous, to show that given function is continuous; we have to show that left hand limit and right hand limits of functions exists and equal to value of f(a),

limx a+fx= limx a-fx=fa.

Definition:

Function f(x) is said to be continuous at a if,

1. faexist,

2. limx afxexists if and only if limx a+fx= limx a-fx

3. limx afx=f(a).

2) Given:

fx=1-x2     if x<11x            if <

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