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

The limit as x approaches 3 of (x-3)/(9-x^2) is -1/6

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

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

- \frac{1}{6}

Decimal Notation

- 0.16666 \dots

Solution steps

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

Simplify

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

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

Plug in the value

x = 3

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

Simplify

= - \frac{1}{6}

\frac{d}{d x} ((x^{3} + 2 x) e^{x})

x \to 1000 lim (x^{\frac{4}{3}})

e^{x^{x}}

\int_{- 1}^{1} (x^{2} - \frac{1}{3})^{2} d x

\int \frac{5 x ^{2}}{( 3 + x ^{3} ) ^{2}} d x

What is the limit as x approaches 3 of (x-3)/(9-x^2) ?
The limit as x approaches 3 of (x-3)/(9-x^2) is -1/6