Question

(2) Consider the function f(x,y) = cos y + sin y (a) Compute the local linearization of f(x,y) at (0,5). (b) Compute the quadratic polynomial for f(x,y) at (0,). (c) Compare the values of the linear and quadratic approximations in part (a) and (b) with the true values for f(,y) at the points (0.007,), (0,0.7924) and (0.7 ). Which approximation gives the closest values ?

Answer 1

solution Hasy) = sytsing 19) el=lt 2 + x + auto- Sinds X- .... Cosxe 1- + - -- f(x,y)= tt Take power 2 term ty from a bore series. (b) f(x,) = 1+2+3 itxt thy 42 y non term from . Take power 2 above series. 10,0.7924), (0.7, 1) (6) true value at 10.007, 17/ f(x,y) True value 0.71207 0.70712 2.01375 Unear Model 0.56049 0.55791 0.66127 0.68183 0.67638 1.45464 quadratic model HX+22 Tty y z b) gines. Near values

please rate as high as you can