EXERCISE SET 4.1 1. Use the forward-difference formulas and backward-difference formulas to determine each missing entry in the following tables. a. f(x) f'(x) 0.5 0.4794 0.6 0.5646 0.7 0.6442 b. x f(x) | f'(x) 0.0 0.00000 0.2 0.74140 0.4 1.3718 2. Use the forward-difference formulas and backward-difference formulas to determine each missing entry in the following tables. a. x f(x) | f'(x) -0.3 1.9507 -0.1 2.0421 -0.1 2.0601 b. xf(x) f'(x) 1.0 1.0000 1.2 1.2625 1.4 1.6595 3. The data in Exercise I were taken from the following functions. Compute the actual errors in Exercise 1, and find error bounds using the error formulas. a. f(x) = sinx b. f(x)=-2x²+3x-1 4. The data in Exercise 2 were taken from the following functions. Compute the actual errors in Exercise 2 and find error bounds using the error formulas. a. f(x)=2 cos 2x-x b. f(x) = x²lnx+1 5. Use the most accurate three-point formula to determine each missing entry in the following tables. a. x f(x) f'(x) b. x f(x) f'(x) 1.1 9.025013 8.1 16.94410 1.2 11.02318 8.3 17.56492 1.3 13.46374 8.5 18.19056 1.4 16.44465 8.7 18.82091 c. f(x) f'(x) d. f(x) f'(x) 2.9 -4.827866 2.0 3.6887983 3.0 -4.240058 2.1 3.6905701 3.1 -3.496909 3.2 -2.596792 2.2 3.6688192 2.3 3.6245909

Fig: 1