E-AP02 · A small length change in a cube
A cube initially has side 30 cm. Its new side is \(30(1+t)\) cm, where \(0<t\le0.02\).
Use the binomial theorem to write the exact new volume as a polynomial in t.
For \(t=0.01\), find the exact volume, the first-order estimate \(27000(1+3t)\), and its absolute error.
Find the greatest absolute error of the first-order estimate over the stated interval, justifying your answer without calculus.
Complete-answer checking, worked solutions and indicative written criteria.
Open the complete answer form