What is the limit as x approaches 0 of (x-3)/(x^2-9) ?

The limit as x approaches 0 of (x-3)/(x^2-9) is 1/3

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limit as x approaches 0 of (x-3)/(x^2-9)

x \to 0 lim (\frac{x - 3}{x ^{2} - 9})

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

x \to 0 lim (\frac{x - 3}{x ^{2} - 9})

Plug in the value

x = 0

= \frac{0 - 3}{0 ^{2} - 9}

Simplify

\frac{0 - 3}{0 ^{2} - 9} : \frac{1}{3}

= \frac{1}{3}

x \to 0 lim (\frac{x ^{2}}{x + 5})

x \to - \frac{1}{2} lim (- \frac{7}{2 x + 1})

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

x \to - 2 lim ((x^{2} - 4 x + 5)^{2})

x \to 0 + lim (ln (x) \cdot sin (x))

What is the limit as x approaches 0 of (x-3)/(x^2-9) ?
The limit as x approaches 0 of (x-3)/(x^2-9) is 1/3