What is the limit as x approaches 0+of 9xln(x) ?

The limit as x approaches 0+of 9xln(x) is 0

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limit as x approaches 0+of 9xln(x)

x \to 0 + lim (9 x ln (x))

0

Solution steps

x \to 0 + lim (9 x ln (x))

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

= 9 \cdot x \to 0 + lim (x ln (x))

Rewrite for L'Hopital

= 9 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Apply L'Hopital's Rule

= 9 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Simplify

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

= 9 \cdot x \to 0 + lim (- x)

Plug in the value

x = 0

= 9 (- 0)

Simplify

= 0

x \to 4 lim (3 x^{2} + 2 x)

x \to 0 lim (\frac{x}{e ^{- \frac{8}{x}}})

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

x \to 2 lim (- 5 x)

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

What is the limit as x approaches 0+of 9xln(x) ?
The limit as x approaches 0+of 9xln(x) is 0