Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (3+2*n)/|-1+2*n|
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Limit of (3+x^2-4*x)/(-9+x^2)
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Limit of (x^2-3*x)/(-8+x^2)
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Limit of (1+5*x)*(-1+5*x)
- The double integral of:
- x^2/y^2
- Integral of d{x}:
- x^2/y^2
- x^2/y^2
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Identical expressions
- x^ two /y^ two
- x squared divide by y squared
- x to the power of two divide by y to the power of two
- x2/y2
- x²/y²
- x to the power of 2/y to the power of 2
- x^2 divide by y^2
Limit of the function x^2/y^2
The solution
You have entered
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/ 2\
|x |
lim |--|
x->oo| 2|
\y /
$$\lim_{x \to \infty}\left(\frac{x^{2}}{y^{2}}\right)$$
Limit(x^2/y^2, x, oo, dir='-')
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
Rapid solution
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/1 \
oo*sign|--|
| 2|
\y /
$$\infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)}$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(\frac{x^{2}}{y^{2}}\right) = \infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)}$$
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{y^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{y^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{y^{2}}\right) = \frac{1}{y^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{y^{2}}\right) = \frac{1}{y^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{y^{2}}\right) = \infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)}$$
More at x→-oo
$$\lim_{x \to 0^-}\left(\frac{x^{2}}{y^{2}}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{x^{2}}{y^{2}}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\frac{x^{2}}{y^{2}}\right) = \frac{1}{y^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{x^{2}}{y^{2}}\right) = \frac{1}{y^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{x^{2}}{y^{2}}\right) = \infty \operatorname{sign}{\left(\frac{1}{y^{2}} \right)}$$
More at x→-oo