What is the limit as x approaches 0+of 6xln(x) ?

The limit as x approaches 0+of 6xln(x) is 0

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limit as x approaches 0+of 6xln(x)

x \to 0 + lim (6 x ln (x))

0

Solution steps

x \to 0 + lim (6 x ln (x))

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

= 6 \cdot x \to 0 + lim (x ln (x))

Rewrite for L'Hopital

= 6 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Apply L'Hopital's Rule

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

= 6 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Simplify

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

= 6 \cdot x \to 0 + lim (- x)

Plug in the value

x = 0

= 6 (- 0)

Simplify

= 0

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

x \to 4 lim (\frac{x ^{3} - 8 x ^{2} + 18 x - 8}{x - 4})

x \to 0 - lim (\frac{1}{cos ( x )})

x \to - 1 + lim (\frac{ln ( x + 1 )}{x})

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

What is the limit as x approaches 0+of 6xln(x) ?
The limit as x approaches 0+of 6xln(x) is 0