   Chapter 2.3, Problem 1E ### 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

# Given that lim x → 2 f ( x ) = 4 lim x → 2 g ( x ) = − 2 lim x → 2 h ( x ) = 0 find the limits that ex.ist. If the limit does not exist, explain why.(a) lim x → 2 [ f ( x ) + 5 g ( x ) ] (b) lim x → 2 [ g ( x ) ] 3 (c) lim x → 2 f ( x ) (d) lim x → 2 3 f ( x ) g ( x ) (e) lim x → 2 g ( x ) f ( x ) (f) lim x → 2 g ( x ) f ( x )

(a)

To determine

To find: The limit of the function limx2[f(x)+5g(x)].

Explanation

Given:

The value of limx2f(x)=4, limx2g(x)=2 and limx2h(x)=0

Limit Laws:

Suppose that c is a constant and the limits limxaf(x) and limxag(x) exists, then

Limit law 1: limxa[f(x)+g(x)]=limxaf(x)+limxag(x)

Limit law 2: limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 3: limxa[cf(x)]=climxaf(x)

Limit law 4: limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 5: limxaf(x)g(x)=limxaf(x)limxag(x) if limxag(x)0

Limit law 6: limxa[f(x)]n=[limxaf(x)]n where n is a positive integer

(b)

To determine

To find: The limit of the function limx2[g(x)]3.

(c)

To determine

To find: The limit of the function limx2f(x).

(d)

To determine

To find: The limit of the function limx23f(x)g(x)

(e)

To determine

To find: The limit of the function limx2g(x)h(x).

(f)

To determine

To find: The limit of the function limx2g(x)h(x)f(x).

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