How do you find the horizontal asymptote for #g(x)=e^x2#?
Evaluate x at both
So, the right limit, as
However, the left limit does have an asymptote:
So, the left limit, as
hope that helped
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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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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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