What is the limit as x approaches 0+of xln(2x) ?

The limit as x approaches 0+of xln(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 xln(2x)

x \to 0 + lim (x ln (2 x))

0

Solution steps

x \to 0 + lim (x ln (2 x))

Rewrite for L'Hopital

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

Apply L'Hopital's Rule

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

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

Simplify

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

= x \to 0 + lim (- x)

Plug in the value

x = 0

= - 0

Simplify

= 0

\int v^{\frac{1}{2}} d v

\int (x + 2) (x - 1) d x

x \to 0 - lim (x^{9} - \frac{1}{x})

\int (9 x + 11) e^{x} d x

\int \frac{1}{x 1 + 3 x} d x

What is the limit as x approaches 0+of xln(2x) ?
The limit as x approaches 0+of xln(2x) is 0