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  3. 3 points give the taylors series for the function fx...

Question: 3 points give the taylors series for the function fx...

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[3 points] Give the Taylors series for the function f(x) =cos x about the point 0, writing explicitly all terms of the Taylor polynomial t4(x) of degree 4 and the remainder R6. Note that there are only 3 non-zero terms in t4(x). Indicate 140x) and R Note that the remainder involves x and an unknown c. Indicate the (smallest) interval where c lies. [5 points] Using t4(x) approximate cos 1. Indicate the approximate value in 5 significant decimals. Using R6, give an upper bound (as sharp as you can) for the (absolute value of the) error of the approximation to cos 1. Explain how you got the bound.

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