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

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

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limit as x approaches 1 of (x-1)/(sqrt(x)-\sqrt{1)}

x \to 1 lim (\frac{x - 1}{x - 1})

2

Solution steps

x \to 1 lim (\frac{x - 1}{x - 1})

Simplify

= x \to 1 lim (\frac{x - 1}{x - 1})

Rationalize denominator

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

= x \to 1 lim (x + 1)

Plug in the value

x = 1

= 1 + 1

Simplify

= 2

x \to 9 lim (9 - x)

x \to 0 + lim (\frac{9}{x} - ln (x))

x \to 0 lim (\frac{3}{2 x})

x \to 3 lim (x^{3} - 5 x^{2} + 2 x - 1)

x \to 0 lim (x^{a} sin (\frac{1}{x}))

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