What are the equations of the horizontal asymptotes of the graph?

Question

The graph equations: y= #(2x)/(sqrt(x^2-1))#

(a) y = 0 only
(b) y = 1 only
(c) y = 2 only
(d) y = -2 and y = 2 only
(e) y = -1 and y = 1 only

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Answer 1 · 2018-04-06T21:05:24

#color(red)((d)# is correct.

.

#y=(2x)/sqrt(x^2-1)#

Horizontal asymptotes are found by calculating the limit of the function when #x->+-oo# and #y=Constant#:

#Lim_(x->+-oo)(2x)/sqrt(x^2-1)=Lim_(x->+-oo)2/(+-sqrt(1-1/x^2))=2/(+-sqrt(1-0))=+-2#

#y=2# and #y=-2# are the horizontal asymptotes. The graph of the function is:

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