The location of an object moving along the number line at time t seconds is given by:
d(t) = 100 / 5 + 4 sin(t)
where t is assumed to be non-negative.
(a) Calculate the limit; enter the number, -infinity, infinity or DNE (does not exist):
Lim d(t) = ___________
t ----> [infinity]

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lublana lublana · Answer 1 · 2020-02-14T06:37:21+01:00

Answer:

[tex]\infty[/tex]

Step-by-step explanation:

We are given that

[tex]d(t)=\frac{100}{5+4sint}[/tex]

[tex]t=\infty[/tex]

[tex]\lim_{t\rightarrow \infty}d(t)=\lim_{t\rightarrow}\frac{100}{5+4sint}[/tex]

[tex]suppose a=\frac{1}{t}=\frac{1}{\infty}=0[/tex]

[tex]\lim_{a\rightarrow 0}\frac{100}{5+4sin\frac{1}{a}}[/tex]

[tex]\lim_{a\rightarrow 0}\frac{100}{5+\frac{4}{a}\times \frac{sin\frac{1}{a}}{\frac{1}{a}}}[/tex]

We know that [tex]\lim_{x\rightarrow 0}\frac{sinx}{x}=1[/tex]

[tex]\frac{100}{5+\infty}=0[/tex]

[tex]lim_{t\rightarrow\infty}d(t)=\lim_{a\rightarrow 0}\frac{1}{d(a)}[/tex]

[tex]\lim_{t\rightarrow \infty}d(t)=\frac{1}{0}=\infty[/tex]