What is the limit as x approaches 0 of-((1+x^2)^{cot(x)}) ?

The limit as x approaches 0 of-((1+x^2)^{cot(x)}) is -1

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limit as x approaches 0 of-((1+x^2)^{cot(x)})

x \to 0 lim (- ((1 + x^{2})^{c o t (x)}))

- 1

Solution steps

x \to 0 lim (- (1 + x^{2})^{c o t (x)})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - x \to 0 lim ((1 + x^{2})^{c o t (x)})

Apply exponent rules

= - x \to 0 lim (e^{c o t (x) l n (1 + x^{2})})

Apply the Limit Chain Rule:

1

= - 1

\frac{d}{d t} (\frac{( 2 t y )}{3})

y = e^{x}, y = 2 e^{- x} + 1, x = 0

\frac{\partial}{\partial x} (- 4 sin (2 x))

\frac{d y}{d x}, x^{3} + y^{3} = 36

(0, 1), (1, - 3)

What is the limit as x approaches 0 of-((1+x^2)^{cot(x)}) ?
The limit as x approaches 0 of-((1+x^2)^{cot(x)}) is -1