# How do you find the Maclaurin series of #f(x)=sin(x)# ?

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To find the Maclaurin series of ( f(x) = \sin(x) ), you can use the Taylor series expansion centered at ( x = 0 ). The Maclaurin series is a special case of the Taylor series expansion where the center is ( x = 0 ).

The Maclaurin series for ( \sin(x) ) is:

[ \sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!} - \cdots ]

In general, the Maclaurin series for ( \sin(x) ) is the summation of odd powers of ( x ) divided by their respective factorial, alternating in sign starting with positive.

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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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