A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists. Show that each of the following functions has a horizontal asymptote by calculating the given limit. - 12x lim x 00 5 + 2x 12x – 8 lim x -0 x³ + 10x 9x- 15 lim 14 2x2 Vx2 + 13x lim 14 11x Vx2 + 13x lim 14 – 11x

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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A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at
negative infinity exists.
Show that each of the following functions has a horizontal asymptote by calculating the given limit.
- 12x
-
lim
5 + 2x
12x - 8
lim
x→ - o p3 + 10x – 6
x² – 9x
9х — 15
lim
14 – 2x2
Væ² + 13x
lim
14- 11г
Vx2 + 13x
lim
14 11x
Transcribed Image Text:A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists. Show that each of the following functions has a horizontal asymptote by calculating the given limit. - 12x - lim 5 + 2x 12x - 8 lim x→ - o p3 + 10x – 6 x² – 9x 9х — 15 lim 14 – 2x2 Væ² + 13x lim 14- 11г Vx2 + 13x lim 14 11x
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