(a) Apply Lagrange's formula to find the value of x when f(x) = 0 given that...

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(a) Apply Lagrange's formula to find the value of x when f(x) = 0 given that x: 30 34 38 42 f(x): -30 -13 3 18 dy (b) Solve initial value problem = 1 + xy², y(0)=1 for x = 0.4, 0.5 by using Milne's method when it is given that dx x: y: 0.1 1.105 0.2 0.3 1.223 1.355 (a) Apply Lagrange's formula to find the value of x when f(x) = 0 given that x: 30 34 38 42 f(x): -30 -13 3 18 dy (b) Solve initial value problem = 1 + xy², y(0)=1 for x = 0.4, 0.5 by using Milne's method when it is given that dx x: y: 0.1 1.105 0.2 0.3 1.223 1.355