   Chapter 11.1, Problem 78E 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 → − 1 x 2 + 3 x + 2 x 2 + x

To determine

To calculate: The value of limx1x2+3x+2x2+x by L’Hospital’s rule if it applies otherwise use some other method.

Explanation

Given information:

The provided limit is limx1x2+3x+2x2+x.

Formula used:

If f and g are two differentiable functions such that substituting x=a in the expression f(x)g(x) gives indeterminate form 00 or , then limxaf(x)g(x)=limxaf'(x)g'(x).

Calculation:

Consider the limit, limx1x2+3x+2x2+x

Substitute x=1,

(1)2+3(1)+2(1)2+(1)=13+211=00

As, the function is in 00 form. Therefore, L’Hospital’s rule is applicable

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