How to find the asymptotes of #f(x) = 6^(x2)#?
Find the limit in either infinite direction.
Note that this is just a mental process to undergo.
We can check a graph:
graph{6^(x2) [8.535, 13.965, 2.52, 8.73]}
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To find the asymptotes of the function ( f(x) = 6^{x2} ), follow these steps:

Determine vertical asymptotes by identifying any values of ( x ) that would make the function undefined. In this case, since ( 6^{x2} ) is defined for all real numbers, there are no vertical asymptotes.

Find horizontal asymptotes by analyzing the behavior of the function as ( x ) approaches positive or negative infinity. As ( x ) approaches positive infinity, ( 6^{x2} ) increases without bound, so there is no horizontal asymptote in that direction. Similarly, as ( x ) approaches negative infinity, ( 6^{x2} ) approaches zero, indicating a horizontal asymptote at ( y = 0 ).
Therefore, the horizontal asymptote of the function ( f(x) = 6^{x2} ) is ( y = 0 ).
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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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