What is the limit as x approaches 3 of (3-sqrt(12-x))/(x-3) ?

The limit as x approaches 3 of (3-sqrt(12-x))/(x-3) is 1/6

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limit as x approaches 3 of (3-sqrt(12-x))/(x-3)

x \to 3 lim (\frac{3 - 12 - x}{x - 3})

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

x \to 3 lim (\frac{3 - 12 - x}{x - 3})

Multiply by the conjugate of

3 - 12 - x : \frac{x - 3}{3 + 12 - x}

= x \to 3 lim (\frac{\frac{x - 3}{3 + 12 - x}}{x - 3})

Simplify

\frac{\frac{x - 3}{3 + 12 - x}}{x - 3} : \frac{1}{3 + - x + 12}

= x \to 3 lim (\frac{1}{3 + - x + 12})

Plug in the value

x = 3

= \frac{1}{3 + - 3 + 12}

Simplify

\frac{1}{3 + - 3 + 12} : \frac{1}{6}

= \frac{1}{6}

What is the limit as x approaches 3 of (3-sqrt(12-x))/(x-3) ?
The limit as x approaches 3 of (3-sqrt(12-x))/(x-3) is 1/6