Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of ((-2+3*x)/(1+3*x))^(2*x)
-
Limit of (x/(1+2*x))^x
- Limit of n2*(5/2+n/2)
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Limit of (1-cos(4*x))/(1-cos(8*x))
- Derivative of:
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log(1/x)
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Identical expressions
- log(one /x)
- logarithm of (1 divide by x)
- logarithm of (one divide by x)
- log1/x
- log(1 divide by x)
Limit of the function log(1/x)
The solution
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/ 1\ lim log|1*-| x->oo \ x/
$$\lim_{x \to \infty} \log{\left(1 \cdot \frac{1}{x} \right)}$$
Limit(log(1/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
$$\lim_{x \to \infty} \log{\left(1 \cdot \frac{1}{x} \right)} = -\infty$$
$$\lim_{x \to 0^-} \log{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(1 \cdot \frac{1}{x} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(1 \cdot \frac{1}{x} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(1 \cdot \frac{1}{x} \right)} = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-} \log{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(1 \cdot \frac{1}{x} \right)} = 0$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(1 \cdot \frac{1}{x} \right)} = 0$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(1 \cdot \frac{1}{x} \right)} = -\infty$$
More at x→-oo
The graph