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

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

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     /   /  ___\\
     |sin\\/ x /|
 lim |----------|
x->0+|    ___   |
     \  \/ x    /
lim⁡x→0+(sin⁡(x)x)\lim_{x \to 0^+}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) 
Limit(sin(sqrt(x))/(sqrt(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
02468-8-6-4-2-10105-5
Plot the graph
Rapid solution [src] 
1
11
Expand and simplify
One‐sided limits [src] 
     /   /  ___\\
     |sin\\/ x /|
 lim |----------|
x->0+|    ___   |
     \  \/ x    /
lim⁡x→0+(sin⁡(x)x)\lim_{x \to 0^+}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) 
1
11 
= 1
     /   /  ___\\
     |sin\\/ x /|
 lim |----------|
x->0-|    ___   |
     \  \/ x    /
lim⁡x→0−(sin⁡(x)x)\lim_{x \to 0^-}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) 
1
11 
= 1
= 1
Other limits x→0, -oo, +oo, 1
lim⁡x→0−(sin⁡(x)x)=1\lim_{x \to 0^-}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = 1
More at x→0 from the left
lim⁡x→0+(sin⁡(x)x)=1\lim_{x \to 0^+}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = 1
lim⁡x→∞(sin⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = 0
More at x→oo
lim⁡x→1−(sin⁡(x)x)=sin⁡(1)\lim_{x \to 1^-}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = \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{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = \sin{\left(1 \right)}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x)x)=∞\lim_{x \to -\infty}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = \infty
More at x→-oo
Numerical answer [src] 
1.0
1.0
The graph
Limit of the function sin(sqrt(x))/sqrt(x)
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