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

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

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

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

\infty

Solution steps

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

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 + 3 ) + 1}{x ^{2} - 4 x + 4}) = \infty

x \to 2 + lim (\frac{x ( x + 3 ) + 1}{x ^{2} - 4 x + 4}) = \infty

= \infty

x \to 1 lim (\frac{120 x ^{2}}{x ^{2} + 4})

x \to 0 + lim (\frac{6 csc ( x )}{cot ( x )})

x \to - 2 lim ((4 x + 7) (5 x + 9))

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

y \to 2 lim (ln (sin (\frac{π}{y})))

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