Please answer all questions and show work:

11 Let y = f(x) describe the curve produced by O y- 2x - 1 x- + y- - 2y = 7 where f(2) = 3. What is the equation of the O y=5-X tangent line at (2, 3)? O y= 3+5(x-2) Oy=x-1 12 Suppose you wanted to determine the Taylor series for O f(x) = x+1 f(x) = x- + 1. On which function's Taylor series would you base your variable substitution, assuming that you know the Of (x) = x2+x+1 Taylor series of each? O f(x) = (x+ 1)- 1 o f() = +1 13) If you approximate the function O 12 1 (x - 1) for some z bewteen 1 and I f (I) = - near I = 1 with the Taylor O 1 polynomial 25 (X - 1) for some z bewteen 1 and I 1 P (x) = 2 - 2(2 -1)+ 2(2-1)2 - 2(x-1)3, O 8 (x - 1) for some z bewteen 1 and I 1 which of the following is the remainder? O 32-5 (X - 1) for some z bewteen 1 and