What is the limit as x approaches 2 of (x^3-6x^2+12x-8)/(x^4-4x^3+16x-16) ?

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limit as x approaches 2 of (x^3-6x^2+12x-8)/(x^4-4x^3+16x-16)

x \to 2 lim (\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{4} - 4 x ^{3} + 16 x - 16})

\frac{1}{4}

Decimal Notation

0.25

Solution steps

x \to 2 lim (\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{4} - 4 x ^{3} + 16 x - 16})

Simplify

\frac{x ^{3} - 6 x ^{2} + 12 x - 8}{x ^{4} - 4 x ^{3} + 16 x - 16} : \frac{1}{x + 2}

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

Plug in the value

x = 2

= \frac{1}{2 + 2}

Simplify

= \frac{1}{4}

y = x^{2} + 2 x - 6

\frac{d}{d x} (a e^{x} + b e^{- 9 x})

\frac{\partial}{\partial v} (u \cdot cos (v))

\int (x - 2)^{3} d x

\int_{0}^{1} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

What is the limit as x approaches 2 of (x^3-6x^2+12x-8)/(x^4-4x^3+16x-16) ?
The limit as x approaches 2 of (x^3-6x^2+12x-8)/(x^4-4x^3+16x-16) is 1/4