TITLE: limit of a hyperbolic function
QUESTION [0 upvotes]: How to evaluate this limit without using hopital rule:
$$\lim_{c\rightarrow + \infty}{\frac{\text{sinh}\sqrt{c}}{2\sqrt{x}}}$$
Here is what I have done so far:

we know that $\text{sinh}(x)= \frac{e^x-e^{-x}}{2}.$

So applying this to the limit we find :
$$L= \lim_{c\rightarrow +\infty}{\frac{e^{\sqrt{c}}}{2\sqrt{c}}}.$$
(the other part tends to zero.)
So first is my approach right+would this lead me into anything?)
And second how should I complete(any hints?)
Thanks in advance.

REPLY [1 votes]: Since the e-function increases faster than any power function, the limit is $\infty$.
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