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

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

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

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

0

Solution steps

x \to 0 + lim (3 x 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

d er i v a t i v e 3 x ln (15 x)

a re a x^{2} + 2 x + 1, 2 x + 5, [- 2, 2]

d er i v a t i v e f (x) = 2 lo g_{5} (x)

\int \frac{8}{2 + 8 x} d x

d er i v a t i v e 10 6 x^{9} + 9 x^{6}

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