# What is the Maclaurin Series for #tanax#?

# tan ax = ax + 1/3a^3x^3 +2/15a^5x^5 + ...#

The Maclaurin series is given by

We start with the function

Then, we compute the first few derivatives:

Which permits us to form the Maclaurin serie:

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The Maclaurin series for ( \tan(ax) ) is:

[ \tan(ax) = ax + \frac{a^3 x^3}{3} + \frac{2a^5 x^5}{15} + \frac{17a^7 x^7}{315} + \cdots ]

This series expansion is valid for values of ( x ) close to zero.

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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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