please answer the following

Consider the function f(x) = 39x3 + 45x2 + 73x+ c where c is a constant. (1) Find the third degree Taylor polynomial T3 (x) of f(x) centered at 24. Show all your work. (2) What is the error R3 (x) = f(x) - T3(x)? Will you get the same error if T3 (x) is centered elsewhere? Justify your answer. (3) Use Part (1) and Part (2) to find the partial fraction decomposition of 39x3 + 45x2+ 73x + c (x - 24) 3 Show all your work. (Note: if you skip Part (1) and Part (2), you may still find the partial fraction decomposition in the traditional way.) (4) Find a power series representation of 39x3 + 45x2 +73x + c (x - 24) 3 and find its radius of convergence. What is the coefficient in front of x in this power series? Show all your work