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Active Calculus 1st Ed

Activity 8.5.6.
Let \(P_n(x)\) be the \(n\)th order Taylor polynomial for \(\sin(x)\) centered at \(x=0\text{.}\) Determine how large we need to choose \(n\) so that \(P_n(2)\) approximates \(\sin(2)\) to \(20\) decimal places.