What is the limit as x approaches 0+of e^{3xln(x)} ?

The limit as x approaches 0+of e^{3xln(x)} is 1

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limit as x approaches 0+of e^{3xln(x)}

x \to 0 + lim (e^{3 x l n (x)})

1

Solution steps

x \to 0 + lim (e^{3 x l n (x)})

Simplify

e^{3 x l n (x)} : x^{3 x}

= x \to 0 + lim (x^{3 x})

Apply exponent rules

= x \to 0 + lim (e^{3 x l n (x)})

Apply the Limit Chain Rule:

1

= 1

(arctan (6 x))^{2}

\frac{d y}{d x} = - \frac{x}{y}, y (4) = 3

\frac{d y}{d x} = e^{8 x} + 13 y

x \to \frac{π}{3} lim (\frac{2 cos ^{2} ( x ) + 3 cos ( x ) - 2}{2 cos ( x ) - 1})

f (x) = x^{- \frac{1}{3}}

What is the limit as x approaches 0+of e^{3xln(x)} ?
The limit as x approaches 0+of e^{3xln(x)} is 1