   Chapter 4.4, Problem 2E ### 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 → a f ( x ) = 0   lim x → a g ( x ) = 0   lim x → a h ( x ) = 1 lim x → a p ( x ) = ∞   lim x → a q ( x ) = ∞ which of the following limits are indeterminate forms? For those that are not an indeterminate form, evaluate the limit where possible.(a) lim x → a   [ f ( x ) p ( x ) ] (b) lim x → a   [ h ( x ) p ( x ) ] (c) lim x → a   [ p ( x ) q ( x ) ]

(a)

To determine

Whether limxa[f(x)p(x)] is of indeterminate form and if not then evaluate the limits.

Explanation

Given:

The limit functions are, limxaf(x)=0 and limxap(x)= .

Definition used:

If limit function is of the type limxaf(x)g(x) , where both f(x)0 and g(x)0 or both f(x) and g(x) , then the limit may or may not exist, which is called as indeterminate form of limit.

Quotient rule for limits: “Limit of the quotient is quotient of the limits”,

Calculation:

Rearrange the given function in quotient form and then use the Quotient rule

(b)

To determine

Whether limxa[h(x)p(x)] is of indeterminate form and if not then evaluate the limits.

(c)

To determine

Whether limxa[p(x)q(x)] is of indeterminate form and if not then evaluate the limit.

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