What is the limit as x approaches 0 of x/(sqrt(3+x)-\sqrt{3)} ?

The limit as x approaches 0 of x/(sqrt(3+x)-\sqrt{3)} is 2sqrt(3)

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limit as x approaches 0 of x/(sqrt(3+x)-\sqrt{3)}

x \to 0 lim (\frac{x}{3 + x - 3})

23

Decimal

3.46410 \dots

Solution steps

x \to 0 lim (\frac{x}{3 + x - 3})

Rationalize denominator

\frac{x}{3 + x - 3} : x + 3 + 3

= x \to 0 lim (x + 3 + 3)

Plug in the value

x = 0

= 0 + 3 + 3

Simplify

= 23

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What is the limit as x approaches 0 of x/(sqrt(3+x)-\sqrt{3)} ?
The limit as x approaches 0 of x/(sqrt(3+x)-\sqrt{3)} is 2sqrt(3)