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. -13x lim x-0o 6 2x -13/2 9х — 2 lim x--0o x3 + 10x x2- 8x 13 0 12 lim -1/15 5 — 15х2 x->0o x2 + 6х lim 7 0 2x х->о Vx2 6x lim 0 7- 2х

Question
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.
-13x
lim
x-0o 6 2x
-13/2
9х — 2
lim
x--0o x3 + 10x
x2- 8x 13
0
12
lim
-1/15
5 — 15х2
x->0o
x2 + 6х
lim
7
0
2x
х->о
Vx2 6x
lim
0
7- 2х
Expand
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. -13x lim x-0o 6 2x -13/2 9х — 2 lim x--0o x3 + 10x x2- 8x 13 0 12 lim -1/15 5 — 15х2 x->0o x2 + 6х lim 7 0 2x х->о Vx2 6x lim 0 7- 2х

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