Question

evaluate the limit.
\\( \lim _ { t \
ightarrow \infty } \frac { - 10 t ^ { 2 } - 7 t + 2 } { 5 t - 8 } \\)
simplify any fractions in your answer.

Explanation:

Step1: Divide numerator and denominator by \(t\)

$$\lim_{t ightarrow\infty}\frac{- 10t^{2}-7t + 2}{5t-8}=\lim_{t ightarrow\infty}\frac{-10t-7+\frac{2}{t}}{5-\frac{8}{t}}$$

Step2: Apply the limit

As \(t
ightarrow\infty\), \(\lim_{t
ightarrow\infty}\frac{2}{t}=0\) and \(\lim_{t
ightarrow\infty}\frac{8}{t}=0\). So we have \(\lim_{t
ightarrow\infty}\frac{-10t-7 + 0}{5-0}\). Since \(\lim_{t
ightarrow\infty}(-10t-7)=-\infty\)

Answer:

\(-\infty\)