   Chapter 11.1, Problem 86E 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 4 + 20 x 3 1 , 000 x 3 + 6

To determine

To calculate: The value of limx2x4+20x31000x3+6 by L’Hospital’s rule if it applies otherwise use some other method.

Explanation

Given information:

The provided limit is limx2x4+20x31000x3+6.

Formula used:

L’Hospital’s rule:

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).

Closed form function theorem:

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

Calculation:

Consider the limit, limx2x4+20x31000x3+6.

Substitute x= in the function 2x4+20x31000x3+6,

2()4+20()31000()3+6==

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

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