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sin(log(x))
Limit of the function/ sin(log(x))

Limit of the function sin(log(x))

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You have entered [src] 
 lim sin(log(x))
x->0+
lim⁡x→0+sin⁡(log⁡(x))\lim_{x \to 0^+} \sin{\left(\log{\left(x \right)} \right)} 
Limit(sin(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
02468-8-6-4-2-10102.5-2.5
Plot the graph
Other limits x→0, -oo, +oo, 1
lim⁡x→0−sin⁡(log⁡(x))=⟨−1,1⟩\lim_{x \to 0^-} \sin{\left(\log{\left(x \right)} \right)} = \left\langle -1, 1\right\rangle
More at x→0 from the left
lim⁡x→0+sin⁡(log⁡(x))=⟨−1,1⟩\lim_{x \to 0^+} \sin{\left(\log{\left(x \right)} \right)} = \left\langle -1, 1\right\rangle
lim⁡x→∞sin⁡(log⁡(x))=⟨−1,1⟩\lim_{x \to \infty} \sin{\left(\log{\left(x \right)} \right)} = \left\langle -1, 1\right\rangle
More at x→oo
lim⁡x→1−sin⁡(log⁡(x))=0\lim_{x \to 1^-} \sin{\left(\log{\left(x \right)} \right)} = 0
More at x→1 from the left
lim⁡x→1+sin⁡(log⁡(x))=0\lim_{x \to 1^+} \sin{\left(\log{\left(x \right)} \right)} = 0
More at x→1 from the right
lim⁡x→−∞sin⁡(log⁡(x))=⟨−1,1⟩\lim_{x \to -\infty} \sin{\left(\log{\left(x \right)} \right)} = \left\langle -1, 1\right\rangle
More at x→-oo
Rapid solution [src] 
<-1, 1>
⟨−1,1⟩\left\langle -1, 1\right\rangle
Expand and simplify
One‐sided limits [src] 
 lim sin(log(x))
x->0+
lim⁡x→0+sin⁡(log⁡(x))\lim_{x \to 0^+} \sin{\left(\log{\left(x \right)} \right)} 
<-1, 1>
⟨−1,1⟩\left\langle -1, 1\right\rangle 
= -1.20314332687512
 lim sin(log(x))
x->0-
lim⁡x→0−sin⁡(log⁡(x))\lim_{x \to 0^-} \sin{\left(\log{\left(x \right)} \right)} 
<-1, 1>
⟨−1,1⟩\left\langle -1, 1\right\rangle 
= (-4.4841952353385 - 4.11062269554643j)
= (-4.4841952353385 - 4.11062269554643j)
Numerical answer [src] 
-1.20314332687512
-1.20314332687512
The graph
Limit of the function sin(log(x))
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