What is the limit as x approaches 81 of ((sqrt(x)-9))/(x-81) ?

The limit as x approaches 81 of ((sqrt(x)-9))/(x-81) is 1/18

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limit as x approaches 81 of ((sqrt(x)-9))/(x-81)

x \to 81 lim (\frac{( x - 9 )}{x - 81})

\frac{1}{18}

Decimal

0.05555 \dots

Solution steps

x \to 81 lim (\frac{x - 9}{x - 81})

Rationalize numerator

\frac{x - 9}{x - 81} : \frac{1}{x + 9}

= x \to 81 lim (\frac{1}{x + 9})

Plug in the value

x = 81

= \frac{1}{81 + 9}

Simplify

\frac{1}{81 + 9} : \frac{1}{18}

= \frac{1}{18}

What is the limit as x approaches 81 of ((sqrt(x)-9))/(x-81) ?
The limit as x approaches 81 of ((sqrt(x)-9))/(x-81) is 1/18