   Chapter 11, Problem 53RE 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 53-56, find the limit: lim x → + ∞ x 2 e x 2

To determine

To calculate: The value of limit limx+x2ex2.

Explanation

Given information:

The provided limit is limx+x2ex2.

Formula used:

1) 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).

2) The derivative of e raised to a function is ddxeu=eududx.

Calculation:

Consider the limit, limx+x2ex2

Substitute x=+ in the function x2ex2,

(+)2e()2=

As, the function forms form on substituting x=+.

Then, apply l’Hospital’s rule to evaluate the limit as,

limx+x2ex2=limx+ddx(x2)ddxex2

The derivative of e raised to a function is ddxeu=eududx

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