Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(5*x)/(2*x)
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Limit of (3-x)/(-27+x^3)
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Limit of (cos(x)+sin(x))^(1/x)
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Limit of (2/3)^x
- Factor polynomial:
- y^2-x^2
- y^2-x^2
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Identical expressions
- y^ two -x^ two
- y squared minus x squared
- y to the power of two minus x to the power of two
- y2-x2
- y²-x²
- y to the power of 2-x to the power of 2
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Similar expressions
- y^2+x^2
Limit of the function y^2-x^2
The solution
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/ 2 2\ lim \y - x / x->0+
$$\lim_{x \to 0^+}\left(- x^{2} + y^{2}\right)$$
Limit(y^2 - x^2, x, 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
One‐sided limits
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/ 2 2\ lim \y - x / x->0+
$$\lim_{x \to 0^+}\left(- x^{2} + y^{2}\right)$$
2 y
$$y^{2}$$
/ 2 2\ lim \y - x / x->0-
$$\lim_{x \to 0^-}\left(- x^{2} + y^{2}\right)$$
2 y
$$y^{2}$$
y^2
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(- x^{2} + y^{2}\right) = y^{2}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + y^{2}\right) = y^{2}$$
$$\lim_{x \to \infty}\left(- x^{2} + y^{2}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(- x^{2} + y^{2}\right) = y^{2} - 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + y^{2}\right) = y^{2} - 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2} + y^{2}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- x^{2} + y^{2}\right) = y^{2}$$
$$\lim_{x \to \infty}\left(- x^{2} + y^{2}\right) = -\infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(- x^{2} + y^{2}\right) = y^{2} - 1$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- x^{2} + y^{2}\right) = y^{2} - 1$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- x^{2} + y^{2}\right) = -\infty$$
More at x→-oo