What is the limit as x approaches 0+of 8sqrt(x)ln(x) ?

The limit as x approaches 0+of 8sqrt(x)ln(x) is 0

Popular >

limit as x approaches 0+of 8sqrt(x)ln(x)

x \to 0 + lim (8 x ln (x))

0

Solution steps

x \to 0 + lim (8 x ln (x))

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

= 8 \cdot x \to 0 + lim (x ln (x))

Rewrite for L'Hopital

= 8 \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}{2 x ^{\frac{3}{2}}}})

= 8 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{2 x ^{\frac{3}{2}}}})

Simplify

\frac{\frac{1}{x}}{- \frac{1}{2 x ^{\frac{3}{2}}}} : - 2 x^{\frac{1}{2}}

= 8 \cdot x \to 0 + lim (- 2 x^{\frac{1}{2}})

Plug in the value

x = 0

= 8 (- 2 \cdot 0^{\frac{1}{2}})

Simplify

= 0

F (t) = (3 t - 1)^{4} (2 t + 1)^{- 3}

t y^{^{'}} + y = t^{4} y^{3}

\int (a x^{2} + b x + c) d x

y = \frac{2 x - 1}{x + 2}

\frac{d}{d x} (x^{2} (ln (x)))

What is the limit as x approaches 0+of 8sqrt(x)ln(x) ?
The limit as x approaches 0+of 8sqrt(x)ln(x) is 0