Question
Determine whether the function grows faster than $e^{x}$, at the same rate as $e^{x},$ or slower than $e^{x}$ as $x \rightarrow \infty$.$\left(e^{x}+e^{-x}\right) / 2$
Step 1
To do this, we use the definition of rate of growth which involves finding the limit as $x$ approaches infinity of the ratio of the two functions. So we need to find: \[\lim_{x\rightarrow\infty} \frac{\frac{e^x+e^{-x}}{2}}{e^x}\] Show more…
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