What is the limit as x approaches 3 of (sqrt(x+33)-6)/(x-3) ?

The limit as x approaches 3 of (sqrt(x+33)-6)/(x-3) is 1/12

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limit as x approaches 3 of (sqrt(x+33)-6)/(x-3)

x \to 3 lim (\frac{x + 33 - 6}{x - 3})

\frac{1}{12}

Decimal

0.08333 \dots

Solution steps

x \to 3 lim (\frac{x + 33 - 6}{x - 3})

Rationalize numerator

\frac{x + 33 - 6}{x - 3} : \frac{1}{x + 33 + 6}

= x \to 3 lim (\frac{1}{x + 33 + 6})

Plug in the value

x = 3

= \frac{1}{3 + 33 + 6}

Simplify

\frac{1}{3 + 33 + 6} : \frac{1}{12}

= \frac{1}{12}

x \to 2 + lim (\frac{1}{x - 3})

x \to 4 lim (3 x - 5)

x \to \infty lim (- 5, x)

x \to 0 lim (x^{2} \cdot ln (- x))

x \to 2 lim (\frac{4 - 4}{0 \cdot 2 ^{2}})

What is the limit as x approaches 3 of (sqrt(x+33)-6)/(x-3) ?
The limit as x approaches 3 of (sqrt(x+33)-6)/(x-3) is 1/12