What is the limit as t approaches 0 of ((2+t)^3-8)/t ?

The limit as t approaches 0 of ((2+t)^3-8)/t is 12

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limit as t approaches 0 of ((2+t)^3-8)/t

t \to 0 lim (\frac{( 2 + t ) ^{3} - 8}{t})

12

Solution steps

t \to 0 lim (\frac{( 2 + t ) ^{3} - 8}{t})

Simplify

\frac{( 2 + t ) ^{3} - 8}{t} : t^{2} + 6 t + 12

= t \to 0 lim (t^{2} + 6 t + 12)

Plug in the value

t = 0

= 0^{2} + 6 \cdot 0 + 12

Simplify

= 12

x \to - 2 lim (4 x + 1)

\frac{d y}{d t} = - 5 (y - 2)

(x + 1)^{5}

y = \frac{2}{3} x^{\frac{3}{2}}

x 169 - x^{2}

What is the limit as t approaches 0 of ((2+t)^3-8)/t ?
The limit as t approaches 0 of ((2+t)^3-8)/t is 12