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

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

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

x \to 2 lim (\frac{( x - 2 )}{x - 2})

22

Decimal Notation

2.82842 \dots

Solution steps

x \to 2 lim (\frac{x - 2}{x - 2})

Rationalize denominator

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

= x \to 2 lim (x + 2)

Plug in the value

x = 2

= 2 + 2

Simplify

= 22

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x \to 9 lim (lo g_{3} (x))

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