Question: Consider the function f(x) = x e x , tabulated below: (a) Find, exactly, f(1) and f(1). (b) Use the tabulated values and the formula

Consider the function f(x) = x ex, tabulated below:

X 0.96 0.97 0.98 0.99 1.00 f(x) 2.5072 2.5588 2.6112 2.6643 2.7183 x 1.01 1.02 1.03 f(x) 2.7731 2.8287 2.8851

(a) Find, exactly, f´(1) and f"(1).

(b) Use the tabulated values and the formula

f'(a) = (f(a+h)-f(a - h))/2h

to estimate f´(1), for various h. Compute the errors involved and comment on the results.

(c) Repeat (b) for f´´(1) using

f"(a) (f(a+h) - 2f(a) + f(a - h))/h

X 0.96 0.97 0.98 0.99 1.00 f(x) 2.5072 2.5588 2.6112 2.6643 2.7183 x 1.01 1.02 1.03 f(x) 2.7731 2.8287 2.8851 1.04 2.9424

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