Question

Let f have a power series representation, S. Suppose that f(0)=1, f’(0)=3, f’’(0)=2 and f’’’(0)=5. a....

Let f have a power series representation, S. Suppose that f(0)=1, f’(0)=3, f’’(0)=2 and f’’’(0)=5.

a. If the above is the only information we have, to what degree of accuracy can we estimate f(1)?



b. If, in addition to the above information, we know that S converges on the interval [-2,2] and that |f’’’’(x)|< 11 on that interval, then to what degree of accuracy can we estimate f(1)?

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