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The Taylor polynomial for sin(x) for z near 0 to order x is sin(x) = x- e 1 x + -200 + 0(2) 120 This figure shows a plot of sin(x) [blue) and the above Taylor polynomial [red]. (a) Estimate the largest x for which this lower order approximation: 1 sin(2) 3- 6 is accurate to 1%. Obtain an answer within 20% of the true answer. x^5/120 !!! (b) Estimate the largest x for which sin(2) 3 - 1 6 1 + 120 is accurate to 1%. Obtain an answer within 20% of the true answer. Hint: Make sure your answer makes sense when compared to the plot in the previous question. -X^7/7! (c) This is another plot of sin(x) together with a Taylor polynomial approximation to sin(2) near x = 0. What is the largest n for which (-1)" (2n + 1)! 22n+1 is included in the polynomial plotted? 22 (-1)" 22n+1 for various values of n, taking 2 at a point where the two plots are just starting to diverge. Use a computer if you get bored with your calculator Hint: compute (2n+1)!