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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    /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right)$$ 
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
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Rapid solution [src] 
1
$$1$$
Expand and simplify
One‐sided limits [src] 
     /   /  ___\\
     |sin\\/ x /|
 lim |----------|
x->0+|    ___   |
     \  \/ x    /
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right)$$ 
1
$$1$$ 
= 1
     /   /  ___\\
     |sin\\/ x /|
 lim |----------|
x->0-|    ___   |
     \  \/ x    /
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right)$$ 
1
$$1$$ 
= 1
= 1
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = 1$$
$$\lim_{x \to \infty}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = 0$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = \sin{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin{\left(\sqrt{x} \right)}}{\sqrt{x}}\right) = \infty$$
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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