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

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

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        /sin(x)\
 lim log|------|
x->0+   \  x   /
$$\lim_{x \to 0^+} \log{\left(\frac{\sin{\left(x \right)}}{x} \right)}$$ 
Limit(log(sin(x)/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
Plot the graph
Rapid solution [src] 
0
$$0$$
Expand and simplify
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \log{\left(\frac{\sin{\left(x \right)}}{x} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(\frac{\sin{\left(x \right)}}{x} \right)} = 0$$
False

More at x→oo
$$\lim_{x \to 1^-} \log{\left(\frac{\sin{\left(x \right)}}{x} \right)} = \log{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(\frac{\sin{\left(x \right)}}{x} \right)} = \log{\left(\sin{\left(1 \right)} \right)}$$
More at x→1 from the right
False

More at x→-oo
One‐sided limits [src] 
        /sin(x)\
 lim log|------|
x->0+   \  x   /
$$\lim_{x \to 0^+} \log{\left(\frac{\sin{\left(x \right)}}{x} \right)}$$ 
0
$$0$$ 
= 2.92455102785924e-32
        /sin(x)\
 lim log|------|
x->0-   \  x   /
$$\lim_{x \to 0^-} \log{\left(\frac{\sin{\left(x \right)}}{x} \right)}$$ 
0
$$0$$ 
= 2.92455102785924e-32
= 2.92455102785924e-32
Numerical answer [src] 
2.92455102785924e-32
2.92455102785924e-32
The graph
Limit of the function log(sin(x)/x)
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