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

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

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

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

0

Solution steps

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

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (s i n (x))})

Apply the Limit Chain Rule:

0

= 0

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