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

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

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You have entered [src] 
     /  ________\
     |\/ sin(x) |
 lim |----------|
x->oo\    x     /
lim⁡x→∞(sin⁡(x)x)\lim_{x \to \infty}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) 
Limit(sqrt(sin(x))/x, 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
02468-8-6-4-2-10105-5
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Rapid solution [src] 
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Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(sin⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = 0
lim⁡x→0−(sin⁡(x)x)=−∞i\lim_{x \to 0^-}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = - \infty i
More at x→0 from the left
lim⁡x→0+(sin⁡(x)x)=∞\lim_{x \to 0^+}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \infty
More at x→0 from the right
lim⁡x→1−(sin⁡(x)x)=sin⁡(1)\lim_{x \to 1^-}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \sqrt{\sin{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+(sin⁡(x)x)=sin⁡(1)\lim_{x \to 1^+}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = \sqrt{\sin{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sqrt{\sin{\left(x \right)}}}{x}\right) = 0
More at x→-oo
The graph
Limit of the function sqrt(sin(x))/x
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