# What is the Maclaurin series for #e^xsin(x)#?

By proceeding in the same way, we can assess further derivatives.

Just add these values to the Maclaurin series definition.

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

[ e^x \sin(x) = \sum_{n=0}^{\infty} \frac{x^{2n+1}}{(2n+1)!} ]

This series expands the function ( e^x \sin(x) ) around ( x = 0 ).

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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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