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Jinesh jain Asked a Question February 8, 2022 4:13 pm 30 pts Let f(x.y)= =Vv]. Then f:R> R be defined +y If x and y are rational sR)-0o 9. 13. Let by (a.) f, and f, do not exist at (0,0) Otherwise (b.) S. (0,0) =1 Then (c.) f, (0,0) = 0 (a.) f is not continuous at (0,0) (b.) f is continuous at (0,0) but not differentiable at (0,0) (d.) f is differentiable at (0,0)) Let f: R R and g:R R be defined by f(x, y) =ld+|>| and e(x, y) =|. Then 10. (c.) f is differentiable only at (0,0) (a.) f is differentiable at (0, 0), but g is not (d.) f is differentiable every where differentiable at (0, 0) 14. If f(x.y)=/(x+y'), (x.y) #(0,0) 0. (b.) g is differentiable at (0, 0), but f is f(x, y) not differentiable at (0,0) (x.y)= (0,0) (c.) Bothf and g are differentiable at (0, 0) then at (0,0) (a.) f fy do not exist (d.) Both f and g are continuous at (0, 0) (b.) f f, exist and are equal 11. Let y)=y s+)(x )=(00 (y)=(0.0) Then the value of k for which f(x, y) is (c.) The directional derivative exists along any straight line (d.) f is differentiable 15. Let continuous at (0, 0) is f(E9) )+ (0,0):f (0.0) =0 (a.) 0 Then 1 (b.) 2 (a.) f is continuous at (0,0) and the partial derivatives ff, exist at every point of R2 (c.) 1 3 (d.) (b.) f is discontinuous at (0,0) and f. f exist 2xy (x,y) # 0 at every point of R? 12. For (x,y)ER fx, y) = {*+y if (x,y) =0 (c.) f is discontinuous at (0,0) and ff exist 0 Then only at (0,0) (a.) S, and f, exist at (0,0) f is continuous (d.) None of the above at (0,0) 16. The radius of convergence of the power series 2 is (b.) f, and f, exist at (0,0) and f is discontinuous at (0,0) 1=0 (a.) 4 (c.) f, and f, do not exist at (0,0). f is continuous at (0,0) (b.) 1 (d.) f, and f, do not exist at (0,0) and f is discontinuous at (0,0) (c.) 2 (d.) 4

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