What is the limit as x approaches 4 of (3x^2-12x)/(sqrt(x)-2) ?

The limit as x approaches 4 of (3x^2-12x)/(sqrt(x)-2) is 48

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 4 of (3x^2-12x)/(sqrt(x)-2)

x \to 4 lim (\frac{3 x ^{2} - 12 x}{x - 2})

48

Solution steps

x \to 4 lim (\frac{3 x ^{2} - 12 x}{x - 2})

Rationalize denominator

\frac{3 x ^{2} - 12 x}{x - 2} : 3 x (x + 2)

= x \to 4 lim (3 x (x + 2))

Plug in the value

x = 4

= 3 \cdot 4 (4 + 2)

Simplify

3 \cdot 4 (4 + 2) : 48

= 48

x \to 4 lim (3 x^{2} - 2 x)

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

x \to 13 lim (\frac{1}{x - 13})

x \to π lim (9 sin (x))

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

What is the limit as x approaches 4 of (3x^2-12x)/(sqrt(x)-2) ?
The limit as x approaches 4 of (3x^2-12x)/(sqrt(x)-2) is 48