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

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

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

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

- 2 b

Solution steps

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

Rationalize denominator

\frac{b - x}{x - b} : - x - b

= x \to b lim (- x - b)

Plug in the value

x = b

= - b - b

Simplify

= - 2 b

y \to 1 lim (\frac{y ^{11} + 2 y - 3}{y ^{7} + y ^{2} - y - 1})

x \to 1 lim (3 x + 2)

x \to 1 lim (3 x^{2} - 7 x + 2)

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

x \to 0 lim ((2^{x} + x)^{\frac{1}{x}})

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