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

The limit as x approaches 0 of (cos(x))^{csc(x)} is 1

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

x \to 0 lim ((cos (x))^{c s c (x)})

1

Solution steps

x \to 0 lim ((cos (x))^{c s c (x)})

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\frac{d}{d x} (\frac{( - x ^{2} - 1 )}{( x ^{2} - 1 ) ^{2}})

y = 2 x^{3} + 4 x^{2} - x + 2

\int 3 x^{- 1} d x

2 x y d x + (x^{2} - 1) d y = 0

\int_{0}^{\infty} 3 y e^{- 3 y} d y

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