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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

y^{^{'}} - 2 y = 3 e^{2 t}

\frac{\partial}{\partial x} (8 x^{3} y - 7 y^{2} + 2 x)

f (x) = 2 cos (x), at x = \frac{π}{3}

\frac{d}{d x} (x^{2} + 15)

x \to - 2 lim (- 7)

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