The average typing speed S (in words per minute)for a student after t weeks of lessons is given by
$S = \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } }$
What is the limit of S as t approaches infinity?

A) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = \frac { 1 } { 66 }$
B) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = 66$
C) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = 0$
D) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = 160$
E)does not exist

Question

The average typing speed S (in words per minute)for a student after t weeks of lessons is given by 
 $S = \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } }$ 
What is the limit of S as t approaches infinity?

A) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = \frac { 1 } { 66 }$
B) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = 66$
C) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = 0$
D) $\lim _ { t \rightarrow \infty } \frac { 160 t ^ { 2 } } { 66 + t ^ { 2 } } = 160$
E)does not exist

Quizplus · Accepted Answer

As $t$ approaches infinity, the terms without $t$ in the denominator become negligible, so the expression simplifies to $\frac{160t^2}{t^2}$, which simplifies further to 160.

The Average Typing Speed S (In Words Per Minute)for a Student