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How do you find the horizontal asymptote for #g(x)=e^x-2#?

Answer 1

Madelyn Anderson

Evaluate x at both #+-oo#

#""_(xrarroo)^"lim"(e^x-2)=oo#

So, the right limit, as #xrarroo#, has no horizontal asymptote.

However, the left limit does have an asymptote:

#""_(xrarr-oo)^"lim"(e^x-2)=0-2=-2#

So, the left limit, as #xrarr-oo#, has horizontal asymptote #=-2#.

hope that helped

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Answer 2

Madelyn Anderson

To find the horizontal asymptote of the function g(x) = e^x - 2:

Check the behavior of the function as x approaches positive infinity. Since the exponential function e^x grows without bound as x increases, g(x) also grows without bound as x approaches positive infinity.
Check the behavior of the function as x approaches negative infinity. As x approaches negative infinity, e^x approaches 0, and g(x) approaches -2.
Therefore, the horizontal asymptote for g(x) = e^x - 2 is y = -2.

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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.