$\text { Evaluate the limit } \lim _ { x \rightarrow \infty } 7 x \sin \left( \frac { 8 } { x } \right) \text { using L'Hopital's Rule if necessary. }$
A) $\frac { 8 } { 7 }$
B) 56
C) $\infty$
D) 0
E) does not exist

Question

$\text { Evaluate the limit } \lim _ { x \rightarrow \infty } 7 x \sin \left( \frac { 8 } { x } \right) \text { using L'Hopital's Rule if necessary. }$ 
A) $\frac { 8 } { 7 }$
B) 56
C) $\infty$
D) 0
E) does not exist

Quizplus · Accepted Answer

We can first notice that as the denominator of the sine function approaches infinity, the sine function will approach zero. Hence, we are left with evaluating the limit:

$$\lim _ { x \rightarrow \infty } 7x \cdot 0 = 0$$

Therefore, the answer is 0. We do not need to use L'Hopital's Rule.