What is the limit as x approaches 0+of x^3ln(2x) ?

The limit as x approaches 0+of x^3ln(2x) 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 x^3ln(2x)

x \to 0 + lim (x^{3} ln (2 x))

0

Solution steps

x \to 0 + lim (x^{3} ln (2 x))

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{3}{x ^{4}}})

= x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{3}{x ^{4}}})

Simplify

\frac{\frac{1}{x}}{- \frac{3}{x ^{4}}} : - \frac{x ^{3}}{3}

= x \to 0 + lim (- \frac{x ^{3}}{3})

Plug in the value

x = 0

= - \frac{0 ^{3}}{3}

Simplify

- \frac{0 ^{3}}{3} : 0

= 0

x \to 3 lim (x^{2} + 7)

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

x \to 0 lim (\frac{\frac{0}{x ^{2}}}{x})

x \to 1 lim (x^{2} + 4 x - 5)

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

What is the limit as x approaches 0+of x^3ln(2x) ?
The limit as x approaches 0+of x^3ln(2x) is 0