We discussed the process of numerical differentiation using the approximation Using the Taylor series for f(a h) and f(a h) about x a, show that to f(a) with truncation error O(h 6 ) Apply this extrapolation procedure to find f(1) when f(x) cosh x, taking h 0 4, 0 2 and 0 1, working to as many decimal places as your calculator will permit o(h) f(a h) f(a h) 2h

Question: We discussed the process of numerical differentiation using the approximation Using the Taylor series for f(a + h) and f(a h) about x

We discussed the process of numerical differentiation using the approximation

o(h) = f(a+h)-f(ah) 2h

Using the Taylor series for f(a + h) and f(a – h) about x = a, show that

h+ f'(a) = $(h) - f (a)- 5f (a) - .. h 3! 5! and deduce that '(a) = } [40(h) o(h)] + +[(a) + . - Writing (h)

to f´(a) with truncation error O(h⁶). Apply this extrapolation procedure to find f´(1) when f(x) = cosh x, taking h = 0.4, 0.2 and 0.1, working to as many decimal places as your calculator will permit.

o(h) = f(a +h)-f(a - h) 2h

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