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

The limit as x approaches 2 of (x/(x-2))^2 is infinity

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limit as x approaches 2 of (x/(x-2))^2

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

\infty

Solution steps

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

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 2 - lim ((\frac{x}{x - 2})^{2}) = \infty

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

= \infty

x \to \infty lim (\frac{4 x ^{3} + 2 x - 24}{x ^{4} - x ^{2} + 84})

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

x \to 3 lim (\frac{5 - 2 x}{x - 3})

x \to 7 - lim (\frac{x - x}{x - 7})

x \to 5 lim (2 x^{2} - 1)

What is the limit as x approaches 2 of (x/(x-2))^2 ?
The limit as x approaches 2 of (x/(x-2))^2 is infinity