Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1-4*x)^(1/x)
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Limit of (-16+x^2+6*x)/(-2-5*x+3*x^2)
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Limit of (1+x)^(2/3)-(-1+x)^(2/3)
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Limit of 1/3+x/3
- Derivative of:
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log(1+x^2)
- Integral of d{x}:
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log(1+x^2)
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Identical expressions
- log(one +x^ two)
- logarithm of (1 plus x squared )
- logarithm of (one plus x to the power of two)
- log(1+x2)
- log1+x2
- log(1+x²)
- log(1+x to the power of 2)
- log1+x^2
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Similar expressions
- x^(1/3)/log(1+x)^2
- log(1+x^2)/sqrt(x)
- log(1-x^2)
Limit of the function log(1+x^2)
The solution
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/ 2\ lim log\1 + x / x->oo
$$\lim_{x \to \infty} \log{\left(x^{2} + 1 \right)}$$
Limit(log(1 + x^2), 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
$$\lim_{x \to \infty} \log{\left(x^{2} + 1 \right)} = \infty$$
$$\lim_{x \to 0^-} \log{\left(x^{2} + 1 \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(x^{2} + 1 \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(x^{2} + 1 \right)} = \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(x^{2} + 1 \right)} = \log{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(x^{2} + 1 \right)} = \infty$$
More at x→-oo
$$\lim_{x \to 0^-} \log{\left(x^{2} + 1 \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(x^{2} + 1 \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(x^{2} + 1 \right)} = \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(x^{2} + 1 \right)} = \log{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \log{\left(x^{2} + 1 \right)} = \infty$$
More at x→-oo
The graph