What is the limit as x approaches 0+of (sin(x))/(x^{1/2)} ?

The limit as x approaches 0+of (sin(x))/(x^{1/2)} is 0

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limit as x approaches 0+of (sin(x))/(x^{1/2)}

x \to 0 + lim (\frac{sin ( x )}{x ^{\frac{1}{2}}})

0

Solution steps

x \to 0 + lim (\frac{sin ( x )}{x ^{\frac{1}{2}}})

Apply L'Hopital's Rule

= x \to 0 + lim (\frac{cos ( x )}{\frac{1}{2 x ^{\frac{1}{2}}}})

Simplify

= x \to 0 + lim (2 x^{\frac{1}{2}} cos (x))

Plug in the value

x = 0

= 2 \cdot 0^{\frac{1}{2}} cos (0)

Simplify

2 \cdot 0^{\frac{1}{2}} cos (0) : 0

= 0

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What is the limit as x approaches 0+of (sin(x))/(x^{1/2)} ?
The limit as x approaches 0+of (sin(x))/(x^{1/2)} is 0