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Limit of the function/ 2/x

Limit of the function 2/x

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      /2\
 lim  |-|
x->-oo\x/

\lim_{x \to -\infty}\left(\frac{2}{x}\right)

Limit(2/x, x, -oo)

Detail solution

Let's take the limit

\lim_{x \to -\infty}\left(\frac{2}{x}\right)

Let's divide numerator and denominator by x:

\lim_{x \to -\infty}\left(\frac{2}{x}\right)

\lim_{x \to -\infty}\left(\frac{2 \frac{1}{x}}{1}\right)

Do Replacement

u = \frac{1}{x}

then

\lim_{x \to -\infty}\left(\frac{2 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(2 u\right)

0 \cdot 2 = 0

The final answer:

\lim_{x \to -\infty}\left(\frac{2}{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

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Rapid solution [src]

0

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to -\infty}\left(\frac{2}{x}\right) = 0

\lim_{x \to \infty}\left(\frac{2}{x}\right) = 0

\lim_{x \to 0^-}\left(\frac{2}{x}\right) = -\infty

\lim_{x \to 0^+}\left(\frac{2}{x}\right) = \infty

\lim_{x \to 1^-}\left(\frac{2}{x}\right) = 2

\lim_{x \to 1^+}\left(\frac{2}{x}\right) = 2

The graph