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

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

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

x \to 0 + lim ((cot (x))^{s i n (x)})

1

Solution steps

x \to 0 + lim ((cot (x))^{s i n (x)})

Simplify

= x \to 0 + lim (cot^{s i n (x)} (x))

Apply exponent rules

= x \to 0 + lim (e^{s i n (x) l n (c o t (x))})

Apply the Limit Chain Rule:

1

= 1

\frac{d y}{d t} + 2 (t + 1) y^{2} = 0

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x^{2} \frac{d y}{d x} - 2 x y = 3 y^{4}

\int \frac{5}{x} d x

\frac{d}{d x} (e^{(- x^{\frac{1}{2}} + \frac{1}{5} x^{- \frac{3}{5}})})

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