What are all horizontal asymptotes of the graph #y=(5+2^x)/(1-2^x)# ?

Answer 1

Let us find limits at infinity.

#lim_{x to +infty}{5+2^x}/{1-2^x}#

by dividing the numerator and the denominator by #2^x#,

#=lim_{x to +infty}{5/2^x+1}/{1/2^x-1}={0+1}/{0-1}=-1#

and

#lim_{x to -infty}{5+2^x}/{1-2^x}={5+0}/{1-0}=5#

Hence, its horizontal asymptotes are

#y=-1# and #y=5#

They look like this:

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Answer 2

The graph of y=(5+2^x)/(1-2^x) has two horizontal asymptotes. The first one is y=5, and the second one is y=-1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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