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Chapter 14: Q. 20 (page 883)

In Problems 7鈥� 42, find each limit algebraically

limx鈫�-18x5-7x3+8x2+x-4

Short Answer

Expert verified

The value of the limit is2

Step by step solution

01

Step 1. Given Information

The given limit islimx鈫�-18x5-7x3+8x2+x-4

We need to find the value of the limit.

02

Step 2. Expanding the limit

We know,

limx鈫�c[f(x)+g(x)]=limx鈫�cf(x)+limx鈫�cg(x)limx鈫�c[f(x)-g(x)]=limx鈫�cf(x)-limx鈫�cg(x)

Therefore,

limx鈫�-18x5-7x3+8x2+x-4=limx鈫�-18x5-limx鈫�-17x3+limx鈫�-18x2+limx鈫�-1x-limx鈫�-14=8路limx鈫�-1x5-7路limx鈫�-1x3+8路limx鈫�-1x2+limx鈫�-1x-limx鈫�-14

03

Step 3. Substitution of limit

The simplified expression will be

=8路limx鈫�-1x5-7路limx鈫�-1x3+8路limx鈫�-1x2+limx鈫�-1x-limx鈫�-14=8路(-1)5-7路(-1)3+8路(-1)2+(-1)-4=-8+7+8-1-4=2

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