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

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

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

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

2 a

Solution steps

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

Rationalize denominator

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

= x \to a lim (a + x)

Plug in the value

x = a

= a + a

Simplify

= 2 a

x \to + 0 lim (sin (5 x) csc (3 x))

x \to - 2 lim (2 x^{3} + x^{2} - 4)

x \to - 2 lim (2 x^{2} - 8)

x \to 5 + lim (\frac{1}{5 - x})

x \to + 0 lim (x \cdot ln (x))

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