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)

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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

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

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)