Question

Which of the following functions grows the fastest as x grows without bound?

Answer 1

`f(x)=e^x`

Explanation:

First, the function, g(x):

`g(x)=e^(\cos(x))`

The function g(x) oscillates, thus, it does not increase.

The value of 'e' is approximately 2.7.

`\begin{gathered} f(x)=e^x\approx2.7^x \\ h(x)=(2.5)^x \end{gathered}`

Since 2.7 is greater than 2.5, we can infer that f(x) grows the fastest as x grows without bound.