   Chapter 11.1, Problem 82E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 77-88, say whether l’Hospital’s rule applies. If it does, use it to evaluate the given limit. If not use, some other method. lim x → − 2 x 3 + 8 x 2 + 3 x + 2

To determine

To calculate: The value of limx2x3+8x2+3x+2 by l Hospital’s rule if it applies otherwise use some other method.

Explanation

Given information:

The provided limit is limx2x3+8x2+3x+2.

Formula used:

L’Hospital’s rule:

limxaf(x)g(x)=limxaf'(x)g'(x)

Where, f and g are two differentiable functions, when substituting x=a in the expression f(x)g(x) gives indeterminate form 00 or .

Closed form function theorem:

limxaf(x)=f(a)

If f is a closed form function and f(a) is defined, then limxaf(x) exists.

Calculation:

Consider the limit, limx2x3+8x2+3x+2

Substitute x=2 in the function x3+8x2+3x+2,

(2)3+8(2)2+3(2)+2=8+846+2=00

As, the function is in 00 form

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