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

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

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

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

2 b

Solution steps

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

Rationalize denominator

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

= x \to b lim (x + b)

Plug in the value

x = b

= b + b

Simplify

= 2 b

\frac{\partial}{\partial y} (\frac{1}{y})

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

t an g e n t y = x^{3} - 3 x + 3, (3, 21)

x \to \frac{π}{2} lim (\frac{sec ( x )}{sec ( 3 x )})

t an g e n t f (x) = 3 + 4 x^{2} - 2 x^{3}, at x = a

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