Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (-exp(-x)+exp(x))/(exp(x)+exp(-x))
-
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)
- Derivative of:
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log((1+x)/(1-x))
- Integral of d{x}:
- log((1+x)/(1-x))
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Identical expressions
- log((one +x)/(one -x))
- logarithm of ((1 plus x) divide by (1 minus x))
- logarithm of ((one plus x) divide by (one minus x))
- log1+x/1-x
- log((1+x) divide by (1-x))
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Similar expressions
- log((1+x)/(1+x))
- (-2*x+log(1+x)/(1-x))/(x-sin(x))
- log((1-x)/(1-x))
Limit of the function log((1+x)/(1-x))
The solution
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/1 + x\ lim log|-----| x->oo \1 - x/
$$\lim_{x \to \infty} \log{\left(\frac{x + 1}{1 - x} \right)}$$
Limit(log((1 + x)/(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
$$\lim_{x \to \infty} \log{\left(\frac{x + 1}{1 - x} \right)} = i \pi$$
$$\lim_{x \to 0^-} \log{\left(\frac{x + 1}{1 - x} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\frac{x + 1}{1 - x} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\frac{x + 1}{1 - x} \right)} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\frac{x + 1}{1 - x} \right)} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\frac{x + 1}{1 - x} \right)} = i \pi$$
More at x→-oo
$$\lim_{x \to 0^-} \log{\left(\frac{x + 1}{1 - x} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\frac{x + 1}{1 - x} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(\frac{x + 1}{1 - x} \right)} = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\frac{x + 1}{1 - x} \right)} = \infty$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(\frac{x + 1}{1 - x} \right)} = i \pi$$
More at x→-oo
The graph