How do I use a power series to calculate a limit?
This is a straightforward example of using a power series to assess a limit.
dividing the division among the terms,
Since every term is zero except for the first,
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To use a power series to calculate a limit, follow these steps:

Identify the function: Determine the function for which you want to calculate the limit.

Express the function as a power series: Represent the function as a power series by finding its Taylor or Maclaurin series expansion. This involves expressing the function as a sum of terms involving powers of (x) centered around a specific point.

Evaluate the limit: Once you have the function expressed as a power series, substitute the value at which you want to evaluate the limit into the power series.

Determine convergence: Check if the power series converges at the value you're evaluating the limit for. If the series converges, you can use the power series to approximate the limit.

Compute the limit: If the power series converges at the given value, sum up the terms of the series to find the limit.

Verify the result: After computing the limit using the power series, verify your result by comparing it with other methods, such as direct substitution or L'Hôpital's Rule, if applicable.
By following these steps, you can use a power series to calculate a limit for a 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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