Please answer parts 1-5 fully. If possible, please type out your response so I can understand. Thank you!

Taylor Series 1. Suppose f(x) = sin(x) and a = 0 (a) Find the first five derivatives of f(x). f(I) = sin(I) f'(x) = cos(x) f"(x) = -sin(x) f"(I) = f ()(x) = f (x) = (b) Find the value of the derivatives at r = a. f(a) = f(0) = sin(0) = 0 f'(a) = f'(0) = cos(0) = 1 f"(a) = f"(a) = flo) (a) = f(5) (a) =2. Write the formula for the Taylor Series generated by f at r = a. 3. Confirm, complete, or edit the following formula. f(x) = f(0) + 50)( x - ) f(0)(1 - )2 f(0)(x - ) 1! 2! 3! f(x) = 4. Write the formula in summation notation. 5. Write the first four Taylor Polynomials generated by f at x = a. Po(x) = PI(x) = P2(x) = P3(x) =