Mister Exam

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Limit of the function x^2/(2-x)

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

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

Limit(x^2/(2 - x), x, 2)

Detail solution

Let's take the limit

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

transform

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

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

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

False

= -oo

The final answer:

\lim_{x \to 2^+}\left(\frac{x^{2}}{2 - 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

Rapid solution [src]

-oo

-\infty

Expand and simplify

One‐sided limits [src]

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

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

-oo

-\infty

= -608.006622516556

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

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

oo

\infty

= 600.006622516556

= 600.006622516556

Other limits x→0, -oo, +oo, 1

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

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

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

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

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

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

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

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

Numerical answer [src]

-608.006622516556

-608.006622516556

The graph