# How do you find the Maclaurin Series for #f(x)= sin(x+π) #?

Using the formula for trig sum

Then

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To find the Maclaurin series for ( f(x) = \sin(x + \pi) ), we first need to express the function in terms of its Maclaurin series. The Maclaurin series for ( \sin(x) ) is:

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

Substitute ( x + \pi ) for ( x ) in the series:

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

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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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