14. Let an = nsin(3/n), for positive integers n. Then

 

A. 0

B. 1

C. 3

D. 6

E.

 

Solution: The answer is C

Since,

Then,

Notice that the numerator and denominator of the above limit approach zero as n goes to infinity. However, we cannot apply l’Hospital’s Rule since it only relates to functions of real variables. So, let

be the related function and calculate the limit of f(x) as x goes to infinity by applying l’Hospital’s Rule as follows:

Thus,