# How do you find the power series for a function centered at #c# ?

Taylor Series centered at c#

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To find the power series for a function centered at ( c ), you can use the Taylor series expansion. The Taylor series expansion for a function ( f(x) ) centered at ( c ) is given by:

[ f(x) = \sum_{n=0}^{\infty} \frac{{f^{(n)}(c)}}{{n!}}(x-c)^n ]

where ( f^{(n)}(c) ) represents the ( n )-th derivative of ( f(x) ) evaluated at ( x = c ).

To find the power series for a specific function, follow these steps:

- Determine the function ( f(x) ) for which you want to find the power series.
- Calculate the derivatives of ( f(x) ) up to the necessary order.
- Evaluate each derivative at ( x = c ).
- Substitute these values into the Taylor series formula.
- Simplify the series if possible.

This process will give you the power series representation of the function centered at ( c ).

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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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