What is the limit as x approaches 9 of (3-sqrt(x))/(9x-x^2) ?

The limit as x approaches 9 of (3-sqrt(x))/(9x-x^2) is 1/54

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limit as x approaches 9 of (3-sqrt(x))/(9x-x^2)

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

\frac{1}{54}

Decimal Notation

0.01851 \dots

Solution steps

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

Rationalize numerator

\frac{3 - x}{9 x - x ^{2}} : \frac{1}{x ( x + 3 )}

= x \to 9 lim (\frac{1}{x ( x + 3 )})

Plug in the value

x = 9

= \frac{1}{9 ( 9 + 3 )}

Simplify

\frac{1}{9 ( 9 + 3 )} : \frac{1}{54}

= \frac{1}{54}

\int \frac{1}{u ^{2} + 3} d u

\frac{d x}{d y} = \frac{y ^{3} - 3 x}{y}

n = 1 \sum \infty \frac{4}{2 n}

\frac{d ^{3}}{d x ^{3}} (\frac{6}{x ^{2}})

\int (y^{2} cos (x) - 3 x^{2} y - 2 x) d x

What is the limit as x approaches 9 of (3-sqrt(x))/(9x-x^2) ?
The limit as x approaches 9 of (3-sqrt(x))/(9x-x^2) is 1/54