What is the limit as h approaches 0 of (sqrt(2x+2h+1)-sqrt(2x+1))/h ?

The limit as h approaches 0 of (sqrt(2x+2h+1)-sqrt(2x+1))/h is 1/(sqrt(2x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as h approaches 0 of (sqrt(2x+2h+1)-sqrt(2x+1))/h

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

\frac{1}{2 x + 1}

Solution steps

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

Rationalize numerator

\frac{2 x + 2 h + 1 - 2 x + 1}{h} : \frac{2}{2 h + 2 x + 1 + 2 x + 1}

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

Plug in the value

h = 0

= \frac{2}{2 \cdot 0 + 2 x + 1 + 2 x + 1}

Simplify

= \frac{1}{2 x + 1}

What is the limit as h approaches 0 of (sqrt(2x+2h+1)-sqrt(2x+1))/h ?
The limit as h approaches 0 of (sqrt(2x+2h+1)-sqrt(2x+1))/h is 1/(sqrt(2x+1))