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

Limit of the function log(sin(x))

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You have entered [src] 
 lim  log(sin(x))
x->pi+
lim⁡x→π+log⁡(sin⁡(x))\lim_{x \to \pi^+} \log{\left(\sin{\left(x \right)} \right)} 
Limit(log(sin(x)), x, pi)
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
0123456-6-5-4-3-2-1-5050
Plot the graph
One‐sided limits [src] 
 lim  log(sin(x))
x->pi+
lim⁡x→π+log⁡(sin⁡(x))\lim_{x \to \pi^+} \log{\left(\sin{\left(x \right)} \right)} 
-oo
−∞-\infty 
= (-8.84636960921524 + 3.14159265358979j)
 lim  log(sin(x))
x->pi-
lim⁡x→π−log⁡(sin⁡(x))\lim_{x \to \pi^-} \log{\left(\sin{\left(x \right)} \right)} 
-oo
−∞-\infty 
= -8.84633718726286
= -8.84633718726286
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→π−log⁡(sin⁡(x))=−∞\lim_{x \to \pi^-} \log{\left(\sin{\left(x \right)} \right)} = -\infty
More at x→pi from the left
lim⁡x→π+log⁡(sin⁡(x))=−∞\lim_{x \to \pi^+} \log{\left(\sin{\left(x \right)} \right)} = -\infty
lim⁡x→∞log⁡(sin⁡(x))=log⁡(⟨−1,1⟩)\lim_{x \to \infty} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}
More at x→oo
lim⁡x→0−log⁡(sin⁡(x))=−∞\lim_{x \to 0^-} \log{\left(\sin{\left(x \right)} \right)} = -\infty
More at x→0 from the left
lim⁡x→0+log⁡(sin⁡(x))=−∞\lim_{x \to 0^+} \log{\left(\sin{\left(x \right)} \right)} = -\infty
More at x→0 from the right
lim⁡x→1−log⁡(sin⁡(x))=log⁡(sin⁡(1))\lim_{x \to 1^-} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\sin{\left(1 \right)} \right)}
More at x→1 from the left
lim⁡x→1+log⁡(sin⁡(x))=log⁡(sin⁡(1))\lim_{x \to 1^+} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\sin{\left(1 \right)} \right)}
More at x→1 from the right
lim⁡x→−∞log⁡(sin⁡(x))=log⁡(⟨−1,1⟩)\lim_{x \to -\infty} \log{\left(\sin{\left(x \right)} \right)} = \log{\left(\left\langle -1, 1\right\rangle \right)}
More at x→-oo
Numerical answer [src] 
(-8.84636960921524 + 3.14159265358979j)
(-8.84636960921524 + 3.14159265358979j)
The graph
Limit of the function log(sin(x))
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