Find the Maclaurin series for the function f(x)=- and hence that for 1 1+x 1 1+x...

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Find the Maclaurin series for the function f(x)=- and hence that for 1 1+x² 1 1+x f(x)= f(x)= X--+ 3 1 1+x (b) By integrating both sides of the Maclaurin series for . --Σ(-1) (c) Using the Maclaurin series for 5 2n +1 0 f(x)= arctan x up to and including the term with x, show that INT arctan.x dx = 0.158459. (e) Show that the exact value of the integral is 0 1/√3 show that the Maclaurin series for the function f(x)= arctan.x is farctanx dx. -1/2 - 1 (1) . (d) Hence deduce that an approximate value of ㅇ √36 is = 3.14159. (e) To how many decimal places is this approximation expected to be accurate? Find the Maclaurin series for the function f(x)=- and hence that for 1 1+x² 1 1+x f(x)= f(x)= X--+ 3 1 1+x (b) By integrating both sides of the Maclaurin series for . --Σ(-1) (c) Using the Maclaurin series for 5 2n +1 0 f(x)= arctan x up to and including the term with x, show that INT arctan.x dx = 0.158459. (e) Show that the exact value of the integral is 0 1/√3 show that the Maclaurin series for the function f(x)= arctan.x is farctanx dx. -1/2 - 1 (1) . (d) Hence deduce that an approximate value of ㅇ √36 is = 3.14159. (e) To how many decimal places is this approximation expected to be accurate?

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