Question

Lim x-> n/2 (2e^x cos x)

Answer 1

Answer:

A

Step-by-Step Explanation:

We want to find the limit:

$\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}$

Use direct substitution.

Hence:

$\displaystyle{\Rightarrow 2e^\frac{\pi}{2}\cos(\frac{\pi}{2}})$

Recall the unit circle. cos(π/2) is simply 0. Hence:

$\displaystyle{\Rightarrow 2e^\frac{\pi}{2}(0)=0$

Therefore:

$\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}=0$

So, our answer is A.