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

The limit as x approaches 2 of (x^2-4x+4)/(2x^3-3x^2-2x) is 0

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

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

0

Solution steps

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

Simplify

\frac{x ^{2} - 4 x + 4}{2 x ^{3} - 3 x ^{2} - 2 x} : \frac{x - 2}{x ( 2 x + 1 )}

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

Plug in the value

x = 2

= \frac{2 - 2}{2 ( 2 \cdot 2 + 1 )}

Simplify

\frac{2 - 2}{2 ( 2 \cdot 2 + 1 )} : 0

= 0

x \to - \infty lim (x^{3} + 1)

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

x \to 0 lim (x^{2} g (1))

h \to 2 lim (\frac{( 2 + h ) ^{2} - 4}{h})

x \to 0 lim (\frac{8 x ^{2} + 4 x}{x})

What is the limit as x approaches 2 of (x^2-4x+4)/(2x^3-3x^2-2x) ?
The limit as x approaches 2 of (x^2-4x+4)/(2x^3-3x^2-2x) is 0