What is the limit as x approaches 0 of (cos(x))^{cot^2(x)} ?

The limit as x approaches 0 of (cos(x))^{cot^2(x)} is 1/(sqrt(e))

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limit as x approaches 0 of (cos(x))^{cot^2(x)}

x \to 0 lim ((cos (x))^{c o t^{2} (x)})

\frac{1}{e}

Decimal Notation

0.60653 \dots

Solution steps

x \to 0 lim ((cos (x))^{c o t^{2} (x)})

Apply exponent rules

= x \to 0 lim (e^{c o t^{2} (x) l n (c o s (x))})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

ln (\frac{( 1 + x )}{( 1 - x )})

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

\frac{1}{x ^{9}}

\int x (x^{2} - 3)^{4} d x

\frac{d}{d x} (- x + 3)

What is the limit as x approaches 0 of (cos(x))^{cot^2(x)} ?
The limit as x approaches 0 of (cos(x))^{cot^2(x)} is 1/(sqrt(e))