# What is the radius of convergence of the MacLaurin series expansion for #f(x)= sinh x#?

Thus, we observe a fairly regular pattern of ones and zeros alternately. Let's put the series' initial terms in writing:

The expansion of the Maclaurin Series is provided by

Thus, for our purpose, we obtain

When we take out the terms that involve zero, we observe

We'll use the Ratio Test to determine the radius of convergence, where

Remove certain terms from the larger factorial because we want the factorials to cancel each other out:

Thus, we have

So,

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The radius of convergence of the Maclaurin series expansion for ( f(x) = \sinh(x) ) is infinite.

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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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