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

The limit as x approaches 2 of ((x^2-3)/(x^3-4x+2))^2 is 1/4

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

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

\frac{1}{4}

Decimal

0.25

Solution steps

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

Plug in the value

x = 2

= (\frac{2 ^{2} - 3}{2 ^{3} - 4 \cdot 2 + 2})^{2}

Simplify

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

= \frac{1}{4}

x \to 4 + lim (\frac{x - 1}{4 - x})

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

x \to π lim (tan (\frac{5 x}{6}))

x \to 6 lim (x - 1)

x \to 3 lim (\frac{( e ^{2 x} - e ^{6} )}{x - 3})

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