   Chapter 2.3, Problem 50E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Let f ( x ) = { x 2 + 1   if   x < 1 ( x − 2 ) 2   if   x ≥ 1 (a) Find limx→0 −f(x).and lim x→0+ f(x)(b) Does limx→0 f(x) exist?(c) Sketch the graph of f.

(a)

To determine

To find: The limit of the function f(x).

Explanation

Given:

The given function is f(x)={x2+1if x<1(x2)2if x1.

Theorem 1:

The limit limxaf(x)=L if and only if limxaf(x)=L=limxa+f(x).

Obtain the limit of the function f(x) as x approaches left-hand side of 1.

Since f(x)=x2+1 for x<1,

limx1(f(x))=limx1(x2+

(b)

To determine

To find: The limit of the function f(x) as x approaches 1.

(c)

To determine

To sketch: The function f(x)

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