Question

Compare the rates of growth of f(x) = e^(cosx) and g(x) = e^x as x approaches infinity. (4 points)

f(x) grows faster than g(x) as x goes to infinity.
g(x) grows faster than f(x) as x goes to infinity.
f(x) and g(x) grow at the same rate as x goes to infinity.
The rate of growth cannot be determined.

Answer 1

Step-by-step explanation: Answer is B

Answer 2

Recall that cosine will always output a value between -1 and 1.
So your f(x) will never be smaller than e^(-1) and never larger than e^(1).

Meanwhile, your g(x) is growing growing growing.
Nothing is slowing it down.

Therefore, g(x) is growing faster than f(x) as x goes to infinity.