What is the limit as x approaches 9 of (x-sqrt(72+x))/(9-x) ?

The limit as x approaches 9 of (x-sqrt(72+x))/(9-x) is -17/18

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limit as x approaches 9 of (x-sqrt(72+x))/(9-x)

x \to 9 lim (\frac{x - 72 + x}{9 - x})

- \frac{17}{18}

Decimal

- 0.94444 \dots

Solution steps

x \to 9 lim (\frac{x - 72 + x}{9 - x})

Multiply by the conjugate of

x - 72 + x : \frac{x ^{2} - 72 - x}{x + 72 + x}

= x \to 9 lim \frac{\frac{x ^{2} - 72 - x}{x + 72 + x}}{9 - x}

Simplify

\frac{\frac{x ^{2} - 72 - x}{x + 72 + x}}{9 - x} : - \frac{x + 8}{x + x + 72}

= x \to 9 lim (- \frac{x + 8}{x + x + 72})

Plug in the value

x = 9

= - \frac{9 + 8}{9 + 9 + 72}

Simplify

- \frac{9 + 8}{9 + 9 + 72} : - \frac{17}{18}

= - \frac{17}{18}

h \to 2 lim (\frac{1}{4 - h ^{2}})

x \to \infty lim (2 + 3 x)

x \to \infty lim (2^{x} - x)

x \to - 3 + lim (- \frac{x ^{2}}{3 x + 9})

x \to - 3 + lim (9 - x^{2})

What is the limit as x approaches 9 of (x-sqrt(72+x))/(9-x) ?
The limit as x approaches 9 of (x-sqrt(72+x))/(9-x) is -17/18