# What is the Taylor Series Expansion for #sin(sin(x))#?

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Probably a simpler approach overall is to just find the first few nonzero terms by differentiation:

If you felt like finding more nonzero terms, you could use Wolfram Alpha to help you take more derivatives, or enter: Series[sin[sin[x]],{x,0,10}] into it and get:

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The Taylor series expansion for sin(sin(x)) is:

sin(sin(x)) ≈ x - (1/3!)x^3 + (2/5!)x^5 - (5/7!)x^7 + ...

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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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