What is the limit as x approaches-3 of (x^3+27)/(x^2+13x+30) ?

The limit as x approaches-3 of (x^3+27)/(x^2+13x+30) is 27/7

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limit as x approaches-3 of (x^3+27)/(x^2+13x+30)

x \to - 3 lim (\frac{x ^{3} + 27}{x ^{2} + 13 x + 30})

\frac{27}{7}

Decimal

3.85714 \dots

Solution steps

x \to - 3 lim (\frac{x ^{3} + 27}{x ^{2} + 13 x + 30})

Simplify

\frac{x ^{3} + 27}{x ^{2} + 13 x + 30} : \frac{x ^{2} - 3 x + 9}{x + 10}

= x \to - 3 lim (\frac{x ^{2} - 3 x + 9}{x + 10})

Plug in the value

x = - 3

= \frac{( - 3 ) ^{2} - 3 ( - 3 ) + 9}{- 3 + 10}

Simplify

\frac{( - 3 ) ^{2} - 3 ( - 3 ) + 9}{- 3 + 10} : \frac{27}{7}

= \frac{27}{7}

What is the limit as x approaches-3 of (x^3+27)/(x^2+13x+30) ?
The limit as x approaches-3 of (x^3+27)/(x^2+13x+30) is 27/7