What is the limit as x approaches-3 of (x^3-2x^2-8x+21)/(2x^2+x-15) ?

The limit as x approaches-3 of (x^3-2x^2-8x+21)/(2x^2+x-15) is -31/11

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limit as x approaches-3 of (x^3-2x^2-8x+21)/(2x^2+x-15)

x \to - 3 lim (\frac{x ^{3} - 2 x ^{2} - 8 x + 21}{2 x ^{2} + x - 15})

- \frac{31}{11}

Decimal

- 2.81818 \dots

Solution steps

x \to - 3 lim (\frac{x ^{3} - 2 x ^{2} - 8 x + 21}{2 x ^{2} + x - 15})

Simplify

\frac{x ^{3} - 2 x ^{2} - 8 x + 21}{2 x ^{2} + x - 15} : \frac{x ^{2} - 5 x + 7}{2 x - 5}

= x \to - 3 lim (\frac{x ^{2} - 5 x + 7}{2 x - 5})

Plug in the value

x = - 3

= \frac{( - 3 ) ^{2} - 5 ( - 3 ) + 7}{2 ( - 3 ) - 5}

Simplify

\frac{( - 3 ) ^{2} - 5 ( - 3 ) + 7}{2 ( - 3 ) - 5} : - \frac{31}{11}

= - \frac{31}{11}

x \to 2 lim ((2)^{x})

x \to - 4 lim (\frac{∣ x + 2 ∣}{x + 2})

x \to 0 lim (6 (\frac{1}{x} - csc (x)))

x \to 0 lim (\frac{( e ^{2 x} \cdot e ^{3 x} - 1 - 5 x )}{x ^{2}})

x \to 2 lim (\frac{2 - ∣ x ∣}{2 - x})

What is the limit as x approaches-3 of (x^3-2x^2-8x+21)/(2x^2+x-15) ?
The limit as x approaches-3 of (x^3-2x^2-8x+21)/(2x^2+x-15) is -31/11