Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3+sqrt(1+4*x))/(-2+x)
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Limit of 1/(-8+x)
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Limit of (1/x)^(log(1+x)/log(2-x))
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Limit of (1-cos(6*x))/(1-cos(8*x))
- Integral of d{x}:
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x*log(1+x^2)
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Identical expressions
- x*log(one +x^ two)
- x multiply by logarithm of (1 plus x squared )
- x multiply by logarithm of (one plus x to the power of two)
- x*log(1+x2)
- x*log1+x2
- x*log(1+x²)
- x*log(1+x to the power of 2)
- xlog(1+x^2)
- xlog(1+x2)
- xlog1+x2
- xlog1+x^2
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Similar expressions
- x*log(1-x^2)
Limit of the function x*log(1+x^2)
The solution
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/ / 2\\ lim \x*log\1 + x // x->oo
$$\lim_{x \to \infty}\left(x \log{\left(x^{2} + 1 \right)}\right)$$
Limit(x*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
$$\lim_{x \to \infty}\left(x \log{\left(x^{2} + 1 \right)}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \log{\left(x^{2} + 1 \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \log{\left(x^{2} + 1 \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \log{\left(x^{2} + 1 \right)}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \log{\left(x^{2} + 1 \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \log{\left(x^{2} + 1 \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \log{\left(x^{2} + 1 \right)}\right) = \log{\left(2 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \log{\left(x^{2} + 1 \right)}\right) = -\infty$$
More at x→-oo
The graph