   Chapter 2, Problem 3RE ### 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

# Find the limit. lim x → 1 e x 3 − x

To determine

To find: The value of limx1ex3x.

Explanation

Definition 1: “A function f is continuous at a number a if limxaf(x)=f(a)”.

Definition 2: “If f is continuous at b and limxag(x)=b, then limxaf(g(x))=f(b). That is, limxaf(g(x))=f(limxag(x))”.

Calculation:

Obtain the limit of the function by using the definition 2.

Let h(x)=ex3x.

The given function h(x)=f(g(x)) is a composition of two functions namely, f(x)=ex and g(x)=x3x

The exponential function f(x)=ex and the polynomial function g(x)=x3x is continuous everywhere in the domain

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