What is the limit as x approaches 5 of (5-x)/(sqrt(5)-\sqrt{x)} ?

The limit as x approaches 5 of (5-x)/(sqrt(5)-\sqrt{x)} is 2sqrt(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 5 of (5-x)/(sqrt(5)-\sqrt{x)}

x \to 5 lim (\frac{5 - x}{5 - x})

25

Decimal Notation

4.47213 \dots

Solution steps

x \to 5 lim (\frac{5 - x}{5 - x})

Rationalize denominator

\frac{5 - x}{5 - x} : 5 + x

= x \to 5 lim (5 + x)

Plug in the value

x = 5

= 5 + 5

Simplify

= 25

x \to - 2 - lim (x + 6)

x \to 0 + lim (\frac{x + 5}{x})

x \to 5 lim (\frac{\frac{1}{9 x + 9} - \frac{1}{54}}{\frac{1}{9 x + 10} - \frac{1}{55}})

x \to 4 + lim (\frac{2 x - 14}{x - 4})

x \to 7 lim (8 x)

What is the limit as x approaches 5 of (5-x)/(sqrt(5)-\sqrt{x)} ?
The limit as x approaches 5 of (5-x)/(sqrt(5)-\sqrt{x)} is 2sqrt(5)