Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+3*x)^(5/x)
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Limit of x^2/(-2+sqrt(4+x^2))
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Limit of ((5+x^2-6*x)/(5+x^2-5*x))^(2+3*x)
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Limit of (2+x^2+3*x)/(-4+x^2)
- y^2-x
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Identical expressions
- y^ two -x
- y squared minus x
- y to the power of two minus x
- y2-x
- y²-x
- y to the power of 2-x
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Similar expressions
- y^2+x
- 2+x^2+y^2-x*y
- (x-y^2)/(y^2-x)
Limit of the function y^2-x
The solution
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/ 2 \ lim \y - x/ y->0+
$$\lim_{y \to 0^+}\left(- x + y^{2}\right)$$
Limit(y^2 - x, y, 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
Other limits y→0, -oo, +oo, 1
$$\lim_{y \to 0^-}\left(- x + y^{2}\right) = - x$$
More at y→0 from the left
$$\lim_{y \to 0^+}\left(- x + y^{2}\right) = - x$$
$$\lim_{y \to \infty}\left(- x + y^{2}\right) = \infty$$
More at y→oo
$$\lim_{y \to 1^-}\left(- x + y^{2}\right) = 1 - x$$
More at y→1 from the left
$$\lim_{y \to 1^+}\left(- x + y^{2}\right) = 1 - x$$
More at y→1 from the right
$$\lim_{y \to -\infty}\left(- x + y^{2}\right) = \infty$$
More at y→-oo
More at y→0 from the left
$$\lim_{y \to 0^+}\left(- x + y^{2}\right) = - x$$
$$\lim_{y \to \infty}\left(- x + y^{2}\right) = \infty$$
More at y→oo
$$\lim_{y \to 1^-}\left(- x + y^{2}\right) = 1 - x$$
More at y→1 from the left
$$\lim_{y \to 1^+}\left(- x + y^{2}\right) = 1 - x$$
More at y→1 from the right
$$\lim_{y \to -\infty}\left(- x + y^{2}\right) = \infty$$
More at y→-oo
One‐sided limits
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/ 2 \ lim \y - x/ y->0+
$$\lim_{y \to 0^+}\left(- x + y^{2}\right)$$
-x
$$- x$$
/ 2 \ lim \y - x/ y->0-
$$\lim_{y \to 0^-}\left(- x + y^{2}\right)$$
-x
$$- x$$
-x