E-AP04 · A symmetric approximation and a sharp interval
Let \(Q(x)=(1+x)^5+(1-x)^5\), where x is real.
Find the complete simplified expression for Q.
Use \(2+20x^2\) to estimate \(Q(0.02)\). Give the exact absolute error.
Find the largest \(\delta\ge0\) such that the absolute error is at most \(\displaystyle \frac5{128}\) for every \(|x|\le\delta\). Explain why your value is the largest.
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