   Chapter 10.1, Problem 33E 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 5–34, estimate the given limit numerically if it exists. [HINT: See Examples 1–3.] lim x → − ∞ ( x 10 + 2 x 5 + 1 ) e x

To determine

To calculate: The value of limx(x10+2x5+1)ex, if it exists.

Explanation

Given Information:

The provided limit is limx(x10+2x5+1)ex.

Formula used:

The limit limxf(x) exists when x approaches to , f(x) converges to a finite point or diverges to infinity.

Calculation:

Consider the provided expression, limx(x10+2x5+1)ex

Where, f(x)=(x10+2x5+1)ex

Substitute x=10 in f(x)=(x10+2x5+1)ex:

f(10)=((10)10+2(10)5+1)e10=(10102(10)5+1)4.53999×105=(10000000000200000+1)4.5399×105=9999800001453999.29×105=4.53990

Substitute x=100 in f(x)=(x10+2x5+1)ex:

f(100)=((100)10+2(100)5+1)e100=(100102(100)5+1)3.72007×1044=3.72008×1024

Substitute x=1000 in f(x)=(x10+2x5+1)ex:

f(1000)=((1000)10+2(1000)5+1)e1000=(1000102(1000)5+1)5

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