(1) Consider the function f: R³ where k is a positive constant. →R given by f(x, y, z)= sin(x + y) cos(z) /x² + y² + z²

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1 Consider The Function F R Where K Is A Positive Constant R Given By F X Y Z Sin X Y Cos Z X Y Z 1 (200.93 KiB) Viewed 12 times

(1) Consider the function f: R³ where k is a positive constant. →R given by f(x, y, z)= sin(x + y) cos(z) /x² + y² + z² lim (x,y,z) 0 0 (a) Find all values of k> 0 for which f is continuous at the origin. In other words, find all positive real numbers k for which exists and is finite. For each such value, what is f (0, 0, 0)? lim t-0 if (x, y, z) (0,0,0), V if (x, y, z)=(0, 0, 0), sin(x + y) cos(z) x² + y² +2² (b) Find all values of k> 0 for which fr (0, 0, 0) exists. In other words, find all positive real numbers k for which (c) What are fz (0, 0, 0) and fy (0, 0, 0)? Do those values depend on k? f(t,0,0)-f(0,0,0) 0.