Solve the examplesShow please the steps in differentiation and integration parts also

b) b) b) (This is problem 3 from the textbook.) Find a power series representation for the function and determine the radius ofconvergence. 1 f0')=1+x (This is problem l3.a. from the textbook.) Use part a) and differentiation to nd a power series representation for the function and determine the radius of convergence. .906) = m Use part a) and integration to nd a power series representation for the function and determine the radius of convergence. h(x) = ln(1 + x) (Note: let x = 0 to determine the constant C) Find a power series representation for the function and determine the radius ofconvergence. f(x)= 1+:r2 Use part a) and differentiation to find a power series representation for the function and determine the radius of convergence. .906) = m Use part a) and integration to find a power series representation for the function and determine the radius of convergence. Mac) = tan1(x) (Note: let x = 0 to determine the constant C) Find a power series representation for the function and determine the radius of convergence. ftx) = 1 52: Use part a) and differentiation to find a power series representation for the function and determine the radius of convergence. .906) = W (This is problem 15 from the textbook.) Use part a) and integration to find a power series representation for the function and determine the radius of convergence. h(x) = ln(5 x) (Note: let x = 0 to determine the constant C) (This is problem 25 from the textbook.) Evaluate the indefinite integral as a power series. What is the radius ofconvergence? i t 1133