What is the limit as x approaches 1 of (x^2-1)/(sqrt(2x+1)-\sqrt{3)} ?

The limit as x approaches 1 of (x^2-1)/(sqrt(2x+1)-\sqrt{3)} is 2sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 1 of (x^2-1)/(sqrt(2x+1)-\sqrt{3)}

x \to 1 lim (\frac{x ^{2} - 1}{2 x + 1 - 3})

23

Decimal Notation

3.46410 \dots

Solution steps

x \to 1 lim (\frac{x ^{2} - 1}{2 x + 1 - 3})

Rationalize denominator

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

= x \to 1 lim (\frac{( x + 1 ) ( 2 x + 1 + 3 )}{2})

Plug in the value

x = 1

= \frac{( 1 + 1 ) ( 2 \cdot 1 + 1 + 3 )}{2}

Simplify

\frac{( 1 + 1 ) ( 2 \cdot 1 + 1 + 3 )}{2} : 23

= 23

2 lo g_{5} (t)

(y - x 5) d x + (x + y 5) d y = 0

\int sin^{2} (θ) cos (θ) d θ

\int \frac{( 3 x - 2 ) ^{2} + ( 3 x + 2 ) ^{2}}{x ^{2}} d x

\frac{cos ( 2 x )}{sin ( 2 x )}

What is the limit as x approaches 1 of (x^2-1)/(sqrt(2x+1)-\sqrt{3)} ?
The limit as x approaches 1 of (x^2-1)/(sqrt(2x+1)-\sqrt{3)} is 2sqrt(3)