What is the limit as x approaches-3 of (2x^2+5x-3)/(x^2-9) ?

The limit as x approaches-3 of (2x^2+5x-3)/(x^2-9) is 7/6

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limit as x approaches-3 of (2x^2+5x-3)/(x^2-9)

x \to - 3 lim (\frac{2 x ^{2} + 5 x - 3}{x ^{2} - 9})

\frac{7}{6}

Decimal

1.16666 \dots

Solution steps

x \to - 3 lim (\frac{2 x ^{2} + 5 x - 3}{x ^{2} - 9})

Simplify

\frac{2 x ^{2} + 5 x - 3}{x ^{2} - 9} : \frac{2 x - 1}{x - 3}

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

Plug in the value

x = - 3

= \frac{2 ( - 3 ) - 1}{- 3 - 3}

Simplify

\frac{2 ( - 3 ) - 1}{- 3 - 3} : \frac{7}{6}

= \frac{7}{6}

x \to \infty lim (\frac{x ^{2} + 1}{x + 2})

x \to \infty lim (10 x [ln (x + 9) - ln (x)])

x \to 5 lim (x^{2} - 12 x)

x \to 6 lim (\frac{6 - ∣ x ∣}{6 + x})

y \to 0 lim ((cos (8 y)) \frac{1}{y ^{2}})

What is the limit as x approaches-3 of (2x^2+5x-3)/(x^2-9) ?
The limit as x approaches-3 of (2x^2+5x-3)/(x^2-9) is 7/6