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

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

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

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

0

Solution steps

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

Simplify

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

= u \to - 2 lim (\frac{u ( u + 2 )}{u - 3})

Plug in the value

u = - 2

= \frac{( - 2 ) ( - 2 + 2 )}{- 2 - 3}

Simplify

\frac{( - 2 ) ( - 2 + 2 )}{- 2 - 3} : 0

= 0

x \to 0 + lim (\frac{1}{x} + 5 x^{3} + 3)

x \to - 7 lim (\frac{x ^{2} + 16 x + 35}{x ^{2} + 10 x + 21})

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

x \to 7 + lim (\frac{x ^{2} - 4 x - 21}{∣ x - 7 ∣})

x \to 0 lim ((1 + 3 x)^{- \frac{5}{x}})

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