# How do you find the maclaurin series expansion of #sin^3 (x)#?

This is the process of building a Maclaurin series.

Only the first three non-zero terms will I complete.

Thus, the series' continuation is

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To find the Maclaurin series expansion of ( \sin^3(x) ), we first use the identity ( \sin^3(x) = (\sin(x))^3 ). Then, we expand ( (\sin(x))^3 ) using the binomial theorem, which states that ( (a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k ).

Expanding ( (\sin(x))^3 ) using the binomial theorem with ( a = \sin(x) ) and ( b = 0 ), we get:

( (\sin(x))^3 = \binom{3}{0}(\sin(x))^3 + \binom{3}{1}(\sin(x))^2(0) + \binom{3}{2}(\sin(x))^1(0)^2 + \binom{3}{3}(\sin(x))^0(0)^3 )

Simplify each term:

( = \sin^3(x) + 0 + 0 + 0 )

Therefore, the Maclaurin series expansion of ( \sin^3(x) ) is simply ( \sin^3(x) ).

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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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