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

The limit as x approaches 0+of xln(x^3) is 0

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

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

0

Solution steps

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

ln (x^{3}) = 3 ln (x)

= x \to 0 + lim (x \cdot 3 ln (x))

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

= 3 \cdot x \to 0 + lim (x ln (x))

Rewrite for L'Hopital

= 3 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Apply L'Hopital's Rule

= 3 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Simplify

\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}} : - x

= 3 \cdot x \to 0 + lim (- x)

Plug in the value

x = 0

= 3 (- 0)

Simplify

= 0

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

\int_{- 1}^{3} 2 x + 3 - x^{2} d x

\frac{d}{d x} ((arctan (6 x))^{2})

x \to 0 lim (\frac{6 x ^{2} + 6 x}{x})

f (x) = 4 x^{- \frac{1}{8}}

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