What is the limit as x approaches-3 of (x^3+x^2-21x-45)/(x^3+7x^2+15x+9) ?

The limit as x approaches-3 of (x^3+x^2-21x-45)/(x^3+7x^2+15x+9) is 4

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limit as x approaches-3 of (x^3+x^2-21x-45)/(x^3+7x^2+15x+9)

x \to - 3 lim (\frac{x ^{3} + x ^{2} - 21 x - 45}{x ^{3} + 7 x ^{2} + 15 x + 9})

4

Solution steps

x \to - 3 lim (\frac{x ^{3} + x ^{2} - 21 x - 45}{x ^{3} + 7 x ^{2} + 15 x + 9})

Simplify

\frac{x ^{3} + x ^{2} - 21 x - 45}{x ^{3} + 7 x ^{2} + 15 x + 9} : \frac{x - 5}{x + 1}

= x \to - 3 lim (\frac{x - 5}{x + 1})

Plug in the value

x = - 3

= \frac{- 3 - 5}{- 3 + 1}

Simplify

= 4

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

x \to - 3 lim (4)

x \to 0.1 lim (x^{x})

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

x \to 2 lim (5 x^{2} - 4 x + 10)

What is the limit as x approaches-3 of (x^3+x^2-21x-45)/(x^3+7x^2+15x+9) ?
The limit as x approaches-3 of (x^3+x^2-21x-45)/(x^3+7x^2+15x+9) is 4