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Limit of the function/ -3/x

Limit of the function -3/x

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     /-3 \
 lim |---|
x->oo\ x /

\lim_{x \to \infty}\left(- \frac{3}{x}\right)

Limit(-3/x, x, oo, dir='-')

Detail solution

Let's take the limit

\lim_{x \to \infty}\left(- \frac{3}{x}\right)

Let's divide numerator and denominator by x:

\lim_{x \to \infty}\left(- \frac{3}{x}\right)

\lim_{x \to \infty}\left(\frac{\left(-1\right) 3 \frac{1}{x}}{1}\right)

Do Replacement

u = \frac{1}{x}

then

\lim_{x \to \infty}\left(\frac{\left(-1\right) 3 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(- 3 u\right)

- 0 = 0

The final answer:

\lim_{x \to \infty}\left(- \frac{3}{x}\right) = 0

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

Plot the graph

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty}\left(- \frac{3}{x}\right) = 0

\lim_{x \to 0^-}\left(- \frac{3}{x}\right) = \infty

\lim_{x \to 0^+}\left(- \frac{3}{x}\right) = -\infty

\lim_{x \to 1^-}\left(- \frac{3}{x}\right) = -3

\lim_{x \to 1^+}\left(- \frac{3}{x}\right) = -3

\lim_{x \to -\infty}\left(- \frac{3}{x}\right) = 0

Rapid solution [src]

0

Expand and simplify

The graph