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cos(x)*log(x)
Limit of the function/ cos(x)*log(x)

Limit of the function cos(x)*log(x)

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You have entered [src] 
 lim (cos(x)*log(x))
x->0+
lim⁡x→0+(log⁡(x)cos⁡(x))\lim_{x \to 0^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) 
Limit(cos(x)*log(x), x, 0)
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
02468-8-6-4-2-1010-1010
Plot the graph
One‐sided limits [src] 
 lim (cos(x)*log(x))
x->0+
lim⁡x→0+(log⁡(x)cos⁡(x))\lim_{x \to 0^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) 
-oo
−∞-\infty 
= -8.85888306270682
 lim (cos(x)*log(x))
x->0-
lim⁡x→0−(log⁡(x)cos⁡(x))\lim_{x \to 0^-}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) 
-oo
−∞-\infty 
= (-8.8553295008311 + 3.13695664871034j)
= (-8.8553295008311 + 3.13695664871034j)
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(log⁡(x)cos⁡(x))=−∞\lim_{x \to 0^-}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = -\infty
More at x→0 from the left
lim⁡x→0+(log⁡(x)cos⁡(x))=−∞\lim_{x \to 0^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = -\infty
lim⁡x→∞(log⁡(x)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
More at x→oo
lim⁡x→1−(log⁡(x)cos⁡(x))=0\lim_{x \to 1^-}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = 0
More at x→1 from the left
lim⁡x→1+(log⁡(x)cos⁡(x))=0\lim_{x \to 1^+}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = 0
More at x→1 from the right
lim⁡x→−∞(log⁡(x)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\log{\left(x \right)} \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
More at x→-oo
Numerical answer [src] 
-8.85888306270682
-8.85888306270682
The graph
Limit of the function cos(x)*log(x)
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