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Approximating derivatives f(z +h) - f(z) f(x)-f( -h) f(x + h) - f(x - h) Forward difference Backward difference Centered diff2. Write a short program that uses formulas (1), (3) and (4) to approximate f(1) and f(1) for f(x)e with h 1, 2-1, 2-2,.., 2

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Approximating derivatives f(z +h) - f(z) f(x)-f( -h) f(x + h) - f(x - h) Forward difference Backward difference Centered difference for 1st derivative s(a) (3) 2h t)-2e-bCentered diference for 2nd derivative (4) 2
2. Write a short program that uses formulas (1), (3) and (4) to approximate f(1) and f"(1) for f(x)e with h 1, 2-1, 2-2,.., 2-60. Format your output in columns as follows: h (6+f)() error (öf(1 error f error Indicate the values of h (in each coln) that give the least error (where, as usual, the error is the absolute δ f) (1) error (52 f)(1 value of the difference between the exact value, of the derivative, and the approximate value)
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