# How to find the Taylor series for the function #cosh(z)*cos(z)# about the point 0 ?

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NOTE:

Making use of the identity

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To find the Taylor series for the function (\cosh(z) \cdot \cos(z)) about the point (0), we use the Taylor series expansions for (\cosh(z)) and (\cos(z)), and then multiply them together term by term. The Taylor series expansions are:

[\cosh(z) = \sum_{n=0}^{\infty} \frac{z^{2n}}{(2n)!}] [\cos(z) = \sum_{n=0}^{\infty} \frac{(-1)^n z^{2n}}{(2n)!}]

Multiply the two series together term by term, remembering that (i \cdot i = -1). Then, simplify the resulting expression to get the Taylor series for (\cosh(z) \cdot \cos(z)) about the point (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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