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x*log(1+x^2)
Limit of the function/ x*log(1+x^2)

Limit of the function x*log(1+x^2)

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 lim \x*log\1 + x //
x->oo
lim⁡x→∞(xlog⁡(x2+1))\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
02468-8-6-4-2-1010-100100
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Rapid solution [src] 
oo
∞\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(xlog⁡(x2+1))=∞\lim_{x \to \infty}\left(x \log{\left(x^{2} + 1 \right)}\right) = \infty
lim⁡x→0−(xlog⁡(x2+1))=0\lim_{x \to 0^-}\left(x \log{\left(x^{2} + 1 \right)}\right) = 0
More at x→0 from the left
lim⁡x→0+(xlog⁡(x2+1))=0\lim_{x \to 0^+}\left(x \log{\left(x^{2} + 1 \right)}\right) = 0
More at x→0 from the right
lim⁡x→1−(xlog⁡(x2+1))=log⁡(2)\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→1+(xlog⁡(x2+1))=log⁡(2)\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→−∞(xlog⁡(x2+1))=−∞\lim_{x \to -\infty}\left(x \log{\left(x^{2} + 1 \right)}\right) = -\infty
More at x→-oo
The graph
Limit of the function x*log(1+x^2)
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