Divide numerator and denominator by the highest power of x in the denominator to find the limit.
-$$\lim _ { t\rightarrow \infty } \frac { \sqrt { 4 t ^ { 2 } - 8 } } { t - 2 }$$
A) 4
B) 2
C) does not exist
D) 8

Question

Divide numerator and denominator by the highest power of x in the denominator to find the limit.
-$$\lim _  { t\rightarrow \infty } \frac { \sqrt { 4 t ^ { 2 } - 8 } } { t - 2 }$$
A) 4
B) 2
C) does not exist
D) 8

Quizplus · Accepted Answer

The highest power of $t$ in the denominator is $t^1$. Dividing both numerator and denominator by $t$ gives $\lim _ { t\rightarrow \infty } \frac { \sqrt { 4 - 8/t^2 } } { 1 - 2/t }$. As $t \rightarrow \infty$, the terms $-8/t^2$ and $-2/t$ approach 0, simplifying the expression to $\sqrt{4}/1 = 2$.

Divide Numerator and Denominator by the Highest Power of X lim⁡t→∞4t2−8t−2\lim _ { t\rightarrow \infty } \frac { \sqrt { 4 t ^ { 2 } - 8 } } { t - 2 }t→∞lim​t−24t2−8​​

Divide Numerator and Denominator by the Highest Power of X $\lim _ { t\rightarrow \infty } \frac { \sqrt { 4 t ^ { 2 } - 8 } } { t - 2 }$