For the part highlighted in green, why doesn't negative infinitiy cancel with the negative near the x, and give us infinity? Instead it gives us 0. I know a number to thr negative infinity power is 0, just thought 2 negatives made a positive so was wondering why not here. And also, would thus converge or diverge?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
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For the part highlighted in green, why doesn't negative infinitiy cancel with the negative near the x, and give us infinity? Instead it gives us 0. I know a number to thr negative infinity power is 0, just thought 2 negatives made a positive so was wondering why not here. And also, would thus converge or diverge?

8.9.27
.
dx
lim
+ lim
%3D
xe
0.
0.
1
1
lim
6 -00
+ lim
%3D
e
0.
1
1
62
2
= lim
1
1
+ lim
%3D
0.
2.
tan-1
(b tan-1s
9.
9.
Transcribed Image Text:8.9.27 . dx lim + lim %3D xe 0. 0. 1 1 lim 6 -00 + lim %3D e 0. 1 1 62 2 = lim 1 1 + lim %3D 0. 2. tan-1 (b tan-1s 9. 9.
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