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

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

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

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

0

Solution steps

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

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

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

Simplify

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

= x \to 0 + lim (- x)

Plug in the value

x = 0

= - 0

Simplify

= 0

\frac{6 x}{5 - cot ( x )}

e^{2 x^{2 x}}

x \to 1 lim ((x - 1)^{- 1})

f (x) = cos^{3} (x), at (0)

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

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