1Q. (a) Expand the function into Taylor's Series, to the third order at a=1. (b) Calculate...

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1Q. (a) Expand the function into Taylor's Series, to the third order at a=1. (b) Calculate the approximated value at x= 0.25. 2Q. Use the bisection method and Regula falsi method of finding roots of equations xe* -2=0 use the initial approximations as 0.8 and 0.9 conduct three iterations. 3Q. Find the real root of the given function f(x) = 2x-log(x)-7=0 by Newton-Raphson iterative method and corrected to three decimal places (Take initial approximation as 3.6). 4Q. Find the root of system of equations using Newton Method. Employ initial guesses of x=y=1.2 y=-x+x+0.75 y+5xy = x 5Q. Using Lagrange's interpolation formula, find a cubic polynomial which approximates the following data -8131 1Q. (a) Expand the function into Taylor's Series, to the third order at a=1. (b) Calculate the approximated value at x= 0.25. 2Q. Use the bisection method and Regula falsi method of finding roots of equations xe* -2=0 use the initial approximations as 0.8 and 0.9 conduct three iterations. 3Q. Find the real root of the given function f(x) = 2x-log(x)-7=0 by Newton-Raphson iterative method and corrected to three decimal places (Take initial approximation as 3.6). 4Q. Find the root of system of equations using Newton Method. Employ initial guesses of x=y=1.2 y=-x+x+0.75 y+5xy = x 5Q. Using Lagrange's interpolation formula, find a cubic polynomial which approximates the following data -8131