What is the limit as x approaches 10 of (sqrt(x-1)-3)/(x-10) ?

The limit as x approaches 10 of (sqrt(x-1)-3)/(x-10) is 1/6

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limit as x approaches 10 of (sqrt(x-1)-3)/(x-10)

x \to 10 lim (\frac{x - 1 - 3}{x - 10})

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

x \to 10 lim (\frac{x - 1 - 3}{x - 10})

Rationalize numerator

\frac{x - 1 - 3}{x - 10} : \frac{1}{x - 1 + 3}

= x \to 10 lim (\frac{1}{x - 1 + 3})

Plug in the value

x = 10

= \frac{1}{10 - 1 + 3}

Simplify

\frac{1}{10 - 1 + 3} : \frac{1}{6}

= \frac{1}{6}

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What is the limit as x approaches 10 of (sqrt(x-1)-3)/(x-10) ?
The limit as x approaches 10 of (sqrt(x-1)-3)/(x-10) is 1/6