How do you find the vertical, horizontal or slant asymptotes for #h(x)=5^(x2)#?
Horizontal :
graph{y(y5^x/25)=0 [1.95, 1.948, 0.975, 0.975]}
yintercept ( x = 0 ) : 1/25
So, the xaxis y = 0 is the asymptote.
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To find the vertical, horizontal, or slant asymptotes for the function ( h(x) = 5^{x2} ), follow these guidelines:

Vertical asymptotes: There are no vertical asymptotes for exponential functions.

Horizontal asymptote: To find the horizontal asymptote, consider the behavior of the function as ( x ) approaches positive or negative infinity.
[ \lim_{x \to \pm\infty} 5^{x2} = 5^{2} = \frac{1}{25} ]
So, the horizontal asymptote is ( y = \frac{1}{25} ).
 Slant asymptote: Exponential functions do not have slant asymptotes.
In summary, for the function ( h(x) = 5^{x2} ):
 There are no vertical asymptotes.
 The horizontal asymptote is ( y = \frac{1}{25} ).
 There are no slant asymptotes.
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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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