(1) Consider the function f: R³ R given by where k is a positive constant. f(x, y, z) sin (2 + y) cos(z) x² + y² +2² 0 (

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1 Consider The Function F R R Given By Where K Is A Positive Constant F X Y Z Sin 2 Y Cos Z X Y 2 0 1 (128.05 KiB) Viewed 13 times

(1) Consider the function f: R³ R given by where k is a positive constant. f(x, y, z) sin (2 + y) cos(z) x² + y² +2² 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)? if (x, y, z) = (0,0,0), sin(x + y) cos(z) (x,y,z) 0 √x² + y² + 2² lim lim 4-0 if (x, y, z) = (0,0,0), (b) Find all values of k> 0 for which f (0, 0, 0) exists. In other words, find all positive real numbers k for which (c) What are f(0, 0, 0) and f, (0, 0, 0)? Do those values depend on k? f(t,0,0)-f(0,0,0) 0.