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

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

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

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

0

Solution steps

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

ln (x^{6}) = 6 ln (x)

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

\frac{6 x}{( x + 1 )}

\int \frac{7 x ^{2} + x + 54}{x ^{3} + 9 x} d x

y = x + 2

\frac{d}{d x} (\frac{5}{25 x ^{2} + 1})

\int \frac{2 t ^{5}}{5} - \frac{2 t ^{2}}{5} - \frac{2 t}{5} d t

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