# What is the taylor series expansion for the tangent function (tanx)?

# tan x = x + 1/3x^3 +2/15x^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 Taylor series expansion for the tangent function (tanx) centered around x = 0 is:

tan(x) = x + (x^3)/3 + (2x^5)/15 + (17x^7)/315 + ... + ((2^(2n) * (2^(2n) - 1) * B_{2n} * x^(2n-1))/(2n)!) + ...

where B_{2n} are the Bernoulli numbers and n! denotes the factorial of n.

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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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