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

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

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

x \to 0 + lim (g (x) (x)^{c o t (x)})

0

Solution steps

x \to 0 + lim (g (x) x^{c o t (x)})

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

With the exception of indeterminate form

= x \to 0 + lim (g (x)) \cdot x \to 0 + lim (x^{c o t (x)})

x \to 0 + lim (g (x)) = g (0)

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

= g \cdot 0 \cdot 0

Simplify

= 0

x \to - \infty lim (3 x e^{x})

x \to 2 lim (\frac{x + 1}{x + 2})

x \to 1 lim (arccos (\frac{1}{x + 1}))

x \to 0 + lim (\frac{x}{e ^{- \frac{1}{x}}})

x \to 2 lim (6 x^{2} + 3 x - 9)

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