What is the limit as x approaches 2 of (x^3-2x^2-6x+12)/(x^2+3x-10) ?

The limit as x approaches 2 of (x^3-2x^2-6x+12)/(x^2+3x-10) is -2/7

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limit as x approaches 2 of (x^3-2x^2-6x+12)/(x^2+3x-10)

x \to 2 lim (\frac{x ^{3} - 2 x ^{2} - 6 x + 12}{x ^{2} + 3 x - 10})

- \frac{2}{7}

Decimal Notation

- 0.28571 \dots

Solution steps

x \to 2 lim (\frac{x ^{3} - 2 x ^{2} - 6 x + 12}{x ^{2} + 3 x - 10})

Simplify

\frac{x ^{3} - 2 x ^{2} - 6 x + 12}{x ^{2} + 3 x - 10} : \frac{x ^{2} - 6}{x + 5}

= x \to 2 lim (\frac{x ^{2} - 6}{x + 5})

Plug in the value

x = 2

= \frac{2 ^{2} - 6}{2 + 5}

Simplify

= - \frac{2}{7}

x \to \infty lim (4 e^{- x} + 6 x - 3)

x \to 9 - lim (\frac{x}{x ^{2} - 81})

x \to 0 + lim (e^{x^{x}})

x \to 0 lim ((1 + 6 x)^{\frac{1}{x}})

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

What is the limit as x approaches 2 of (x^3-2x^2-6x+12)/(x^2+3x-10) ?
The limit as x approaches 2 of (x^3-2x^2-6x+12)/(x^2+3x-10) is -2/7