Question

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

Answer 1

A

Step-by-Step Explanation:

We want to find the limit:

`\displaystyle{\lim_{x\to(\pi)/(2)}(2e^x\cos(x))}`

Use direct substitution.

Hence:

`\displaystyle{\Rightarrow 2e^(\pi)/(2)\cos((\pi)/(2)})`

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

`\displaystyle{\Rightarrow 2e^(\pi)/(2)(0)=0`

Therefore:

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

So, our answer is A.