Question

The location of an object moving along the number line at time t seconds is given by:

Answer 1

Answer:

$\infty$

Step-by-step explanation:

We are given that

$d(t)=\frac{100}{5+4sint}$

$t=\infty$

$\lim_{t\rightarrow \infty}d(t)=\lim_{t\rightarrow}\frac{100}{5+4sint}$

$suppose a=\frac{1}{t}=\frac{1}{\infty}=0$

$\lim_{a\rightarrow 0}\frac{100}{5+4sin\frac{1}{a}}$

$\lim_{a\rightarrow 0}\frac{100}{5+\frac{4}{a}\times \frac{sin\frac{1}{a}}{\frac{1}{a}}}$

We know that $\lim_{x\rightarrow 0}\frac{sinx}{x}=1$

$\frac{100}{5+\infty}=0$

$lim_{t\rightarrow\infty}d(t)=\lim_{a\rightarrow 0}\frac{1}{d(a)}$

$\lim_{t\rightarrow \infty}d(t)=\frac{1}{0}=\infty$