Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-4+x^2)/(x^3+2*x)
-
Limit of (x^2-11*x)/x
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Limit of (1+x)/x^2
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Limit of 1+(1+x)^2/x^2
- Derivative of:
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x^2/(1-x)
- Integral of d{x}:
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x^2/(1-x)
- Graphing y =:
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x^2/(1-x)
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Identical expressions
- x^ two /(one -x)
- x squared divide by (1 minus x)
- x to the power of two divide by (one minus x)
- x2/(1-x)
- x2/1-x
- x²/(1-x)
- x to the power of 2/(1-x)
- x^2/1-x
- x^2 divide by (1-x)
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Similar expressions
- (-4+x^2)/(1-x-sqrt(3))
- x^2/(1+x)
Limit of the function x^2/(1-x)
The solution
You have entered
[src]
/ 2 \
| x |
lim |-----|
x->1+\1 - x/
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
Limit(x^2/(1 - x), x, 1)
Detail solution
Let's take the limit
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
transform
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
=
$$\lim_{x \to 1^+}\left(- \frac{x^{2}}{x - 1}\right) = $$
The final answer:
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right) = -\infty$$
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
transform
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
=
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
=
$$\lim_{x \to 1^+}\left(- \frac{x^{2}}{x - 1}\right) = $$
False
= -oo
The final answer:
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right) = -\infty$$
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->1+\1 - x/
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right)$$
-oo
$$-\infty$$
= -153.006622516556
/ 2 \
| x |
lim |-----|
x->1-\1 - x/
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{1 - x}\right)$$
oo
$$\infty$$
= 149.006622516556
= 149.006622516556
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{1 - x}\right) = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x^{2}}{1 - x}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{1 - x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{1 - x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{1 - x}\right) = \infty$$
More at x→-oo
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{1 - x}\right) = -\infty$$
$$\lim_{x \to \infty}\left(\frac{x^{2}}{1 - x}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{1 - x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{1 - x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{1 - x}\right) = \infty$$
More at x→-oo
The graph