Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
-
Limit of 10+x^2+3*x^3+8*x
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Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
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Limit of (-4+x^2)/(x^3+2*x)
- Derivative of:
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x^2/(2-x)
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Identical expressions
- x^ two /(two -x)
- x squared divide by (2 minus x)
- x to the power of two divide by (two minus x)
- x2/(2-x)
- x2/2-x
- x²/(2-x)
- x to the power of 2/(2-x)
- x^2/2-x
- x^2 divide by (2-x)
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Similar expressions
- x^2/(2+x)
- (1+2*x+2*x^2)/(2-x+4*x^3)
Limit of the function x^2/(2-x)
The solution
You have entered
[src]
/ 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
$$\lim_{x \to 2^+}\left(\frac{x^{2}}{2 - x}\right)$$
=
$$\lim_{x \to 2^+}\left(\frac{x^{2}}{2 - x}\right)$$
=
$$\lim_{x \to 2^+}\left(- \frac{x^{2}}{x - 2}\right) = $$
The final answer:
$$\lim_{x \to 2^+}\left(\frac{x^{2}}{2 - x}\right) = -\infty$$
$$\lim_{x \to 2^+}\left(\frac{x^{2}}{2 - x}\right)$$
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
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
$$\lim_{x \to 2^-}\left(\frac{x^{2}}{2 - x}\right) = -\infty$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x^{2}}{2 - x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x^{2}}{2 - x}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{2 - x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{2 - x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{2 - x}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{2 - x}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{2 - x}\right) = \infty$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\frac{x^{2}}{2 - x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x^{2}}{2 - x}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{2 - x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{2 - x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{2 - x}\right) = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{2 - x}\right) = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{2 - x}\right) = \infty$$
More at x→-oo
The graph