Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 10+x^2+3*x^3+8*x
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Limit of (-2+sqrt(x))/(-4+x^2)
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Limit of x+2*x^3+5*x^4-x^2/3
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Limit of (-x^3+2*x+5*x^4)/(1+x^4-8*x^3)
- Integral of d{x}:
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1/(x*log(x))
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Identical expressions
- one /(x*log(x))
- 1 divide by (x multiply by logarithm of (x))
- one divide by (x multiply by logarithm of (x))
- 1/(xlog(x))
- 1/xlogx
- 1 divide by (x*log(x))
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Similar expressions
- 1/(x*log(x)*sqrt(log(log(x))))
- (1+1/x)^log(x)
- (-1+e^(1/x))*log(x)
- 1/(x*log(x)^2)
Limit of the function 1/(x*log(x))
The solution
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1 lim -------- x->oox*log(x)
$$\lim_{x \to \infty} \frac{1}{x \log{\left(x \right)}}$$
Limit(1/(x*log(x)), 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
The graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \frac{1}{x \log{\left(x \right)}} = 0$$
$$\lim_{x \to 0^-} \frac{1}{x \log{\left(x \right)}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x \log{\left(x \right)}} = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x \log{\left(x \right)}} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x \log{\left(x \right)}} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x \log{\left(x \right)}} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \frac{1}{x \log{\left(x \right)}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \frac{1}{x \log{\left(x \right)}} = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \frac{1}{x \log{\left(x \right)}} = -\infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \frac{1}{x \log{\left(x \right)}} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \frac{1}{x \log{\left(x \right)}} = 0$$
More at x→-oo
The graph