Consider the function f : R² R given by:

c2k y' cos(x2 + y?) , if (x, y) # (0, 0) f(Ex, y) = O , if (x, y) = (0, 0) where k is a positive constant. (a) Find all values of & for which f is continuous at (0, 0). In other words, find all values of * for which y' cos(x2 + y?) lim(z,y) +0 = 0. Justify your answer.(b) Recall that the partial derivative of f with respect to y at a point {:n..._ if} in the domain of f is . .. 'lJ-vi' t" _ ,1, .'...l E. f9 l,_r.'_'I-;i1_l limit:4] f if I. 'T i it _n_ i'l . Using our expression for f, nd all values of is for which the partial derivative f i '11-. f] f {If}, n) Emsv.3 f exists. For these values of is, what is the value \"233'. {:U} {1:}