Question

Find the limit of the function by using direct substitution.


limit as x approaches quantity pi divided by 2 of quantity 2e^x sin x

The choices are:
a. 0
b. 2e^(pi/2)
c. 1
d. pi/2

Answer 1

Answer:

b. 2e^(pi/2)

Step-by-step explanation:

We have to evaluate the following expression by using direct substitution:

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

Substituting the value of x, we get:

$2e^{\frac{\pi}{2} } sin(\frac{\pi}{2} )$

Since, the value of sin(π/2) = 1, the above expression will be reduced to:

$2e^{\frac{\pi}{2} }$

Therefore, option b gives the correct answer

Answer 2

The answer I would choose is b). Pi/2