The Taylor polynomial Pn(x) about 0 approximates f(x) with error En(x) and the Taylor series converges to f(x). Find the smallest constant K given by the alternating series error bound such that |E4(1)| ≤ K for f(x) = cosx. NOTE: Enter the exact answer or approximate to five decimal places.
![Find the second Taylor polynomial T2(x) for the function f(x) = cos(x) based at b = π/6. T2(x) = Let a be a positive real number and let J be the closed interval [π/6 - a, π/6 + a]. Use the Quadratic Approximation Error Bound to verify that |f(x) - T2(x)| ≤ a^3/3! for all x in J. Use this error bound to find a value of a so that |f(x) - T2(x)| ≤ 0.01 for all x in J. (Round your answer to six decimal places.) a =](https://www.doubtrix.com/uploads/editor/7211922884LPKkYMSdtJ.png)
![Find the second Taylor polynomial T2(x) for the function f(x) = cos(x) based at b = π6. T2(x) = Let a be a positive real number and let J be the closed interval [π6−a, π6+a]. Use the Quadratic Approximation Error Bound to verify that |f(x)−T2(x)| ≤ a33! for all x in J Use this error bound to find a value of a so that |f(x) − T2(x)| ≤ 0.01 for all x in J. (Round your answer to six decimal places. ) a =](https://www.doubtrix.com/uploads/editor/2518734386VIHUSShwoG.png)
