Question

evaluate the limit.
limₜ→-∞ 6/(-5t - 4)
simplify any fractions in your answer.

Explanation:

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

Divide numerator \(6\) by \(t\) and denominator \(-5t - 4\) by \(t\).
We get \(\lim_{t
ightarrow-\infty}\frac{\frac{6}{t}}{-5-\frac{4}{t}}\).

Step2: Apply the limit rule \(\lim_{t

ightarrow\pm\infty}\frac{c}{t}=0\) (\(c\) is a constant)
As \(t
ightarrow-\infty\), \(\lim_{t
ightarrow-\infty}\frac{6}{t}=0\) and \(\lim_{t
ightarrow-\infty}\frac{4}{t}=0\).
So, \(\frac{\lim_{t
ightarrow-\infty}\frac{6}{t}}{\lim_{t
ightarrow-\infty}(-5)-\lim_{t
ightarrow-\infty}\frac{4}{t}}=\frac{0}{-5 - 0}\).

Answer:

\(0\)