State the name and defining equation for each of the finite difference operators (5 Marks) (i)...

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State the name and defining equation for each of the finite difference operators (5 Marks) (i) 5 (ii) ▼ (iii) A (iv) H (V) E (b) Given f (x) = x3 -x+4 on [0, 10] use h = 2 to draw a backward difference table. (4 Marks) (c) Given y = f (x) a function, derive the second order difference central approximation for f'(x). What is the order of the error in the approximation? (4 Marks) (d) Use a first-order method to approximate f'(1) given f (x) = x2 + 1 with h = 0.2. State the name and defining equation for each of the finite difference operators (5 Marks) (i) 5 (ii) ▼ (iii) A (iv) H (V) E (b) Given f (x) = x3 -x+4 on [0, 10] use h = 2 to draw a backward difference table. (4 Marks) (c) Given y = f (x) a function, derive the second order difference central approximation for f'(x). What is the order of the error in the approximation? (4 Marks) (d) Use a first-order method to approximate f'(1) given f (x) = x2 + 1 with h = 0.2.