$\text { Evaluate the } \lim _ { x \rightarrow \infty } \frac { 5 x ^ { 2 } + 4 x - 8 } { 9 x ^ { 2 } + 9 } \text { using L'Hôpital's Rule if necessary. }$
A) $\frac { 1 } { 2 }$
B) $- \frac { 8 } { 9 }$
C) $\frac { 5 } { 9 }$
D) 0
E) $\infty$

Question

$\text { Evaluate the } \lim _ { x \rightarrow \infty } \frac { 5 x ^ { 2 } + 4 x - 8 } { 9 x ^ { 2 } + 9 } \text { using L'Hôpital's Rule if necessary. }$ 
A) $\frac { 1 } { 2 }$
B) $- \frac { 8 } { 9 }$
C) $\frac { 5 } { 9 }$
D) 0
E) $\infty$

Quizplus · Accepted Answer

We can directly apply the limit here, since both numerator and denominator are polynomial of the same degree. Thus, we can see that the limit equals $\frac{5}{9}$.

A) 12\frac { 1 } { 2 }21​ B) −89- \frac { 8 } { 9 }−98​

A) $\frac { 1 } { 2 }$ B) $- \frac { 8 } { 9 }$