What is the limit as x approaches 25 of (1/(sqrt(x))-1/5)/(x-25) ?

The limit as x approaches 25 of (1/(sqrt(x))-1/5)/(x-25) is -1/250

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limit as x approaches 25 of (1/(sqrt(x))-1/5)/(x-25)

x \to 25 lim (\frac{\frac{1}{x} - \frac{1}{5}}{x - 25})

- \frac{1}{250}

Decimal

- 0.004

Solution steps

x \to 25 lim (\frac{\frac{1}{x} - \frac{1}{5}}{x - 25})

Rationalize numerator

\frac{\frac{1}{x} - \frac{1}{5}}{x - 25} : - \frac{1}{5 x ( x + 5 )}

= x \to 25 lim (- \frac{1}{5 x ( x + 5 )})

Plug in the value

x = 25

= - \frac{1}{5 25 ( 25 + 5 )}

Simplify

- \frac{1}{5 25 ( 25 + 5 )} : - \frac{1}{250}

= - \frac{1}{250}

What is the limit as x approaches 25 of (1/(sqrt(x))-1/5)/(x-25) ?
The limit as x approaches 25 of (1/(sqrt(x))-1/5)/(x-25) is -1/250