Mister Exam

Lang:

Limit of the function/ -3*x

Limit of the function -3*x

You have entered [src]

 lim (-3*x)
x->oo

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

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

Detail solution

Let's take the limit

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

Let's divide numerator and denominator by x:

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

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

Do Replacement

u = \frac{1}{x}

then

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

- \frac{3}{0} = -\infty

The final answer:

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

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(- 3 x\right) = -\infty

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

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

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

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

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

Rapid solution [src]

-oo

-\infty

Expand and simplify

The graph