What is the limit as x approaches 0+of (1+4x)^{cot(x)} ?

The limit as x approaches 0+of (1+4x)^{cot(x)} is e^4

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limit as x approaches 0+of (1+4x)^{cot(x)}

x \to 0 + lim ((1 + 4 x)^{c o t (x)})

e^{4}

Decimal

54.59815 \dots

Solution steps

x \to 0 + lim ((1 + 4 x)^{c o t (x)})

Apply exponent rules

= x \to 0 + lim (e^{c o t (x) l n (1 + 4 x)})

Apply the Limit Chain Rule:

e^{4}

= e^{4}

t a y l or x^{2} + 1

y^{^{'}} = 2 y + 39

d er i v a t i v e f (x) = \frac{4}{x - 2}

x \to 4 - lim (e^{\frac{3}{4 - x}})

\frac{\partial}{\partial x} (x - a)

What is the limit as x approaches 0+of (1+4x)^{cot(x)} ?
The limit as x approaches 0+of (1+4x)^{cot(x)} is e^4