1 Consider The Function F R R Given By Where K Is A Positive Constant F X Y Z Sin X Y Cos Z Y 2 Lim 0 1 (36.97 KiB) Viewed 11 times
1 Consider The Function F R R Given By Where K Is A Positive Constant F X Y Z Sin X Y Cos Z Y 2 Lim 0 2 (10.55 KiB) Viewed 11 times
(1) Consider the function f: R→ R given by where k is a positive constant. f(x, y, z)= sin(x+y) cos(z) +y² +2² lim (₁)-0 (a) Find all values of k> 0 for which f is continuous at the origin. In other words, find all positive real numbers & for which if (x, y, z) (0,0,0), lim if (x, y, z) = (0,0,0), sin(x+y) cos(2) √√²+1² +2² (b) Find all values of k> 0 for which f(0, 0, 0) exists. In other words, find all positive real numbers & for which exists and is finite. For each such value, what is fe(0, 0, 0) f(t,0,0)-f(0,0,0)
(c) What are f(0, 0, 0) and fy (0, 0, 0)? Do those values depend on k?
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