What is the limit as x approaches 0+of (csc(x))^x ?

The limit as x approaches 0+of (csc(x))^x is 1

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limit as x approaches 0+of (csc(x))^x

x \to 0 + lim ((csc (x))^{x})

1

Solution steps

x \to 0 + lim ((csc (x))^{x})

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\frac{\partial}{\partial x} (x \cdot sin (y) \cdot sin (z))

x^{2} + 6 x + 3

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

x \to 8 + lim (ln (x^{2} - 64))

\frac{\partial}{\partial x} (x + \frac{1}{2} y)

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