Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of -cos(x)+5*x
-
Limit of (-30+x^2-x)/(125+x^3)
-
Limit of sin(9*x)
- Limit of cot(pi*x)
- The double integral of:
- y/x
- y/x
- Integral of d{x}:
- y/x
-
Identical expressions
- y/x
- y divide by x
-
Similar expressions
- (x+y)/(x^2+y^2)
- (x-y)/(x+y)^3
- y/(x^2+y^2)
Limit of the function y/x
The solution
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/y\ lim |-| x->0+\x/
$$\lim_{x \to 0^+}\left(\frac{y}{x}\right)$$
Limit(y/x, 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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{y}{x}\right) = \infty \operatorname{sign}{\left(y \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{y}{x}\right) = \infty \operatorname{sign}{\left(y \right)}$$
$$\lim_{x \to \infty}\left(\frac{y}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{y}{x}\right) = y$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{y}{x}\right) = y$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{y}{x}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{y}{x}\right) = \infty \operatorname{sign}{\left(y \right)}$$
$$\lim_{x \to \infty}\left(\frac{y}{x}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{y}{x}\right) = y$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{y}{x}\right) = y$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{y}{x}\right) = 0$$
More at x→-oo
One‐sided limits
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/y\ lim |-| x->0+\x/
$$\lim_{x \to 0^+}\left(\frac{y}{x}\right)$$
oo*sign(y)
$$\infty \operatorname{sign}{\left(y \right)}$$
/y\ lim |-| x->0-\x/
$$\lim_{x \to 0^-}\left(\frac{y}{x}\right)$$
-oo*sign(y)
$$- \infty \operatorname{sign}{\left(y \right)}$$
-oo*sign(y)