4. an automobiles velocity, v, starting from a complete stop is v(t) = 140t / (5t + 3) where v is measured…

4. an automobiles velocity, v, starting from a complete stop is v(t) = 140t / (5t + 3) where v is measured in feet per second. what happens to the autos velocity as time, t, increases? the velocity continues to increase. the velocity approaches 140 feet per second. the velocity approaches 28 feet per second. the velocity begins to decrease. clear all

4. an automobiles velocity, v, starting from a complete stop is v(t) = 140t / (5t + 3) where v is measured in feet per second. what happens to the autos velocity as time, t, increases? the velocity continues to increase. the velocity approaches 140 feet per second. the velocity approaches 28 feet per second. the velocity begins to decrease. clear all

Answer

Explanation:

Step1: Find the limit as t approaches infinity

We want to find $\lim_{t\rightarrow\infty}\frac{140t}{5t + 3}$.

Step2: Divide numerator and denominator by t

$\lim_{t\rightarrow\infty}\frac{140t/t}{(5t + 3)/t}=\lim_{t\rightarrow\infty}\frac{140}{5+\frac{3}{t}}$.

Step3: Evaluate the limit

As $t\rightarrow\infty$, $\frac{3}{t}\rightarrow0$. So $\lim_{t\rightarrow\infty}\frac{140}{5+\frac{3}{t}}=\frac{140}{5}=28$.

Answer:

The velocity approaches 28 feet per second.