What is the limit as x approaches 2 of ((x^3-3x^2+4))/(x^3-7x^2+16x-12) ?

The limit as x approaches 2 of ((x^3-3x^2+4))/(x^3-7x^2+16x-12) is -3

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limit as x approaches 2 of ((x^3-3x^2+4))/(x^3-7x^2+16x-12)

x \to 2 lim (\frac{( x ^{3} - 3 x ^{2} + 4 )}{x ^{3} - 7 x ^{2} + 16 x - 12})

- 3

Solution steps

x \to 2 lim (\frac{x ^{3} - 3 x ^{2} + 4}{x ^{3} - 7 x ^{2} + 16 x - 12})

Simplify

\frac{x ^{3} - 3 x ^{2} + 4}{x ^{3} - 7 x ^{2} + 16 x - 12} : \frac{x + 1}{x - 3}

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

Plug in the value

x = 2

= \frac{2 + 1}{2 - 3}

Simplify

= - 3

x \to - \infty lim (e^{x t})

x \to \infty lim (3 + \frac{6}{x})

b \to \infty lim (sin (b))

x \to - 2 lim (2 - x)

x \to \infty lim (\frac{2 x - 4}{7 x + 6})

What is the limit as x approaches 2 of ((x^3-3x^2+4))/(x^3-7x^2+16x-12) ?
The limit as x approaches 2 of ((x^3-3x^2+4))/(x^3-7x^2+16x-12) is -3