Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
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Limit of ((3+5*x)/(-2+4*x))^(1+3*x)
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Limit of (3+3*x^3+5*x+5*x^2)/(-1+x^2)
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Limit of (3-x^2+5*x)/(4*x^7+81*x)
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Identical expressions
- -log(x)/x^ two
- minus logarithm of (x) divide by x squared
- minus logarithm of (x) divide by x to the power of two
- -log(x)/x2
- -logx/x2
- -log(x)/x²
- -log(x)/x to the power of 2
- -logx/x^2
- -log(x) divide by x^2
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Similar expressions
- log(x)/x^2
Limit of the function -log(x)/x^2
The solution
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[src]
/-log(x) \
lim |--------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right)$$
Limit((-log(x))/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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = \infty$$
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right) = 0$$
More at x→-oo
One‐sided limits
[src]
/-log(x) \
lim |--------|
x->0+| 2 |
\ x /
$$\lim_{x \to 0^+}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right)$$
oo
$$\infty$$
= 114398.997559217
/-log(x) \
lim |--------|
x->0-| 2 |
\ x /
$$\lim_{x \to 0^-}\left(\frac{\left(-1\right) \log{\left(x \right)}}{x^{2}}\right)$$
oo
$$\infty$$
= (114398.997559217 - 71631.4540945009j)
= (114398.997559217 - 71631.4540945009j)
The graph