Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^(4/x)
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Limit of (-6+x^2-x)/(-4+x^2)
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Limit of (-6+x^2-x)/(-21+x+2*x^2)
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Limit of e^(3-x)*(-2+x)
- Sum of series:
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log(1+1/n)
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Identical expressions
- log(one + one /n)
- logarithm of (1 plus 1 divide by n)
- logarithm of (one plus one divide by n)
- log1+1/n
- log(1+1 divide by n)
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Similar expressions
- n*log(1+1/(n*x))
- x*log(1+1/(n*x))
- log(1-1/n)
Limit of the function log(1+1/n)
The solution
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/ 1\ lim log|1 + -| n->oo \ n/
$$\lim_{n \to \infty} \log{\left(1 + \frac{1}{n} \right)}$$
Limit(log(1 + 1/n), n, 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 n→0, -oo, +oo, 1
$$\lim_{n \to \infty} \log{\left(1 + \frac{1}{n} \right)} = 0$$
$$\lim_{n \to 0^-} \log{\left(1 + \frac{1}{n} \right)} = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+} \log{\left(1 + \frac{1}{n} \right)} = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-} \log{\left(1 + \frac{1}{n} \right)} = \log{\left(2 \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \log{\left(1 + \frac{1}{n} \right)} = \log{\left(2 \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \log{\left(1 + \frac{1}{n} \right)} = 0$$
More at n→-oo
$$\lim_{n \to 0^-} \log{\left(1 + \frac{1}{n} \right)} = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+} \log{\left(1 + \frac{1}{n} \right)} = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-} \log{\left(1 + \frac{1}{n} \right)} = \log{\left(2 \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \log{\left(1 + \frac{1}{n} \right)} = \log{\left(2 \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \log{\left(1 + \frac{1}{n} \right)} = 0$$
More at n→-oo
The graph