Assuming 72=0 (-1) 2n (2n)! meets the hypotheses of the Alternating Series Estimation Theorem, (a) find...

  

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Assuming 72=0 (-1) 2n (2n)! meets the hypotheses of the Alternating Series Estimation Theorem, (a) find the range of a such that T(x) = 1-1 + 2! 24 approximates cos(x) with [error] < 0.005. (b) what is the lowest degree Taylor polynomial guaranteed to approximate cos(z) on the interval | < 2 with error] < 10-6? Hint: You will need to use trial and error to find the answer. Be sure to demonstrate you have found the lowest degree by showing both that your choice has sufficiently small error and that the next lowest number of terms would not guarantee a small enough error. Assuming 72=0 (-1) 2n (2n)! meets the hypotheses of the Alternating Series Estimation Theorem, (a) find the range of a such that T(x) = 1-1 + 2! 24 approximates cos(x) with [error] < 0.005. (b) what is the lowest degree Taylor polynomial guaranteed to approximate cos(z) on the interval | < 2 with error] < 10-6? Hint: You will need to use trial and error to find the answer. Be sure to demonstrate you have found the lowest degree by showing both that your choice has sufficiently small error and that the next lowest number of terms would not guarantee a small enough error.