Exercise. This exercise examines qualitative relationships between a function and its Taylor polynomials and explores how the higher order Taylor polynomials naturally "correct" the lower order ones in the context of a specific example. Consider the function f(x) = e2x. Give the first, second, and third degree Taylor polynomials centered at x = 0 below: PI (x) = P2 (2) = P3 (2) = ? Note that each higher order polynomial is the previous lower order polynomial plus a new term. For instance: P3(2) = 1+ 2x+ 2x2 + This is p2(x) This is a new term, which we call a "correction term".Find the first, second, third, and fourth degree Taylor polynomials centered at x = 2 for the function f(x) = In(5 - 2x). P1 (2) = -2(x-2) P2 (x) = - 2 ( x - 2) 12 X P3(x) = -4/3(x-2) ^3 X P4 (2) = -4(X-2) ^4 X