# How do you use a Taylor series to expand: #f(x) = x^2 + 2x + 5# about x = 3?

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To expand ( f(x) = x^2 + 2x + 5 ) about ( x = 3 ) using a Taylor series, follow these steps:

- Find the derivatives of ( f(x) ) up to the desired order.
- Evaluate each derivative at ( x = 3 ).
- Use the Taylor series formula to write the expansion.

The Taylor series expansion of ( f(x) ) about ( x = 3 ) will involve the derivatives of ( f(x) ) evaluated at ( x = 3 ), along with terms involving ( (x - 3) ) raised to the appropriate powers.

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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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