   Chapter 9.1, Problem 10CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 7-10, assume that f, g, and h are polynomials.If g ( c ) ≠ 0 and h ( c ) =   0 , what can be said about lim x → c g ( x ) h ( x ) , and lim x → c h ( x ) g ( x ) ?

To determine

What can be said about limxcg(x)h(x) and limxch(x)g(x) if g(c)0 and h(c)=0.

Explanation

Given Information:

The limits are limxcg(x)h(x) and limxch(x)g(x). The value of g(c)0 and h(c)=0.

Explanation:

Consider the provided limit,

limxcg(x)h(x)

For a rational function, if k is a constant, limxcf(x)=L and limxcg(x)=M, then,

limxcg(x)h(x)=g(c)h(c)

Substitute 0 for h(c) and a non-zero value M for g(c),

limxcg(x)h(x)=a0

Thus, the value of limxcg(x)h(x) is not exist

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