# How do you sketch the curve #f(x)=e^x/(1+e^x)# ?

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So far we have the y-intercept (in blue) and H.A.'s (in green):

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Hence, we have the graph of

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To sketch the curve of ( f(x) = \frac{e^x}{1 + e^x} ):

- Find the domain of the function.
- Determine the behavior of the function as ( x ) approaches positive and negative infinity.
- Find the ( y )-intercept by setting ( x = 0 ).
- Find any vertical asymptotes by solving ( 1 + e^x = 0 ).
- Find any horizontal asymptotes by analyzing the behavior of the function as ( x ) approaches positive and negative infinity.
- Find the critical points by finding where the derivative of the function is zero or undefined.
- Determine the concavity of the function by analyzing the second derivative.
- Sketch the curve using the information gathered from the above steps.

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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.

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.

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.

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