Find the limit.
$$\lim _ { t \rightarrow \infty } \frac { t ^ { 2 } + 3 } { t ^ { 3 } + t ^ { 2 } - 7 }$$
A) $\infty$
B) $- 3$
C) 0
D) 3
E) 7

Question

Quizplus · Accepted Answer

We can use the concept of dominant terms to evaluate the limit. As t approaches infinity, the highest power terms in the numerator and denominator dominate the fraction. In this case, the dominant terms are $t^3$ in the denominator and $t^2$ in the numerator. Therefore, as t approaches infinity, the fraction approaches $\frac{t^2}{t^3}=\frac{1}{t}$. Since $\lim_{t	o\infty}\frac{1}{t}=0$, the answer is (C) 0.

Find the Limit lim⁡t→∞t2+3t3+t2−7\lim _ { t \rightarrow \infty } \frac { t ^ { 2 } + 3 } { t ^ { 3 } + t ^ { 2 } - 7 }t→∞lim​t3+t2−7t2+3​

Find the Limit $\lim _ { t \rightarrow \infty } \frac { t ^ { 2 } + 3 } { t ^ { 3 } + t ^ { 2 } - 7 }$