How to find the asymptotes of #f(x)= (3e^(x))/(22e^(x))#?
Horizontal asymptotes
graph{(3e^x)/(22e^x) [10, 10, 5, 5]}
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To find the asymptotes of ( f(x) = \frac{3e^x}{2  2e^x} ):

Identify the values of ( x ) for which the function is undefined. These are potential vertical asymptotes.

Determine the behavior of the function as ( x ) approaches these values from both sides. This can help identify vertical asymptotes.

Simplify the function and look for any horizontal asymptotes.

Determine the behavior of the function as ( x ) approaches positive and negative infinity. This can help identify horizontal asymptotes.

If there are any oblique (slant) asymptotes, find them by dividing the numerator by the denominator using long division or polynomial division.

Once you have identified all potential asymptotes, verify them by graphing the function.
Following these steps will help in finding the asymptotes of the given function.
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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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