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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0+of 6sqrt(x)ln(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}{2 x ^{\frac{3}{2}}}})

= 6 \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}}

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

Plug in the value

x = 0

= 6 (- 2 \cdot 0^{\frac{1}{2}})

Simplify

= 0

x \to - 2 lim (x^{2} - 4)

\frac{\partial}{\partial x} (2 (y - 5) (x + 5))

\frac{d}{d x} (arcsec (8 x))

\int - cos (x) + sin (x) + 5 d x

\int_{0}^{1} π (x - x^{2}) d x

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