What is the limit as x approaches 0 of (x^2-3x)/(3x) ?

The limit as x approaches 0 of (x^2-3x)/(3x) is -1

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^2-3x)/(3x)

x \to 0 lim (\frac{x ^{2} - 3 x}{3 x})

- 1

Solution steps

x \to 0 lim (\frac{x ^{2} - 3 x}{3 x})

Simplify

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

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

Plug in the value

x = 0

= \frac{1}{3} (0 - 3)

Simplify

\frac{1}{3} (0 - 3) : - 1

= - 1

x \to \infty lim (3 x^{\frac{2}{3}})

x \to 2 - lim (2 x - 2)

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

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

x \to 0 - lim (- 3 x + 2)

What is the limit as x approaches 0 of (x^2-3x)/(3x) ?
The limit as x approaches 0 of (x^2-3x)/(3x) is -1