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###### Jinesh Jain posted an Question
February 08, 2022 • 16:09 pm 30 points
• IIT JAM
• Mathematics (MA)

# Vr-y)- 2 5. let f:r r be defined by 1. the value of lim (x-(22) x-y-4 (a.) 0 s(x)= +y (x.y) (0,0) (b.) 4 (x y) (0.0) at (0.0) (c.) (a.) f is not continuous (b.)

Vr-y)- 2 5. Let f:R R be defined by 1. The value of lim (x-(22) X-y-4 (a.) 0 S(x)= +y (x.y) (0,0) (b.) 4 (x y) (0.0) At (0.0) (C.) (a.) f is not continuous (b.) f is continuous, and both f, and f,exist (d.) (c.) fis differentiable 2 Let f: R2 R be defined by (d) f. and f,exist but f is not differentiable y2 if r+ y#0 6 For r,yeR f(x,y) ={x+y all let if y =0. f(. 9)=x-y' sin (1/ y) if y#0. 0 ifx+y =0 02f2f Ox dy oy dx Then the value of at the Then at the point (0, 0), (a.) s is NOT continuous point (0, 0) is (b.) f is continuous but NOT differentiable (a.) 0 f (b.) 1 (c.)exists butdoes NOT exist dy (c.) 2 (d.) f is differentiable (d.) 4 7. For all (x. y)e R?, let 3 The function f(r,y)=3x2y + 4y3 -3x2 -12y2 +1 has a saddle point at +y if x#0, f(. ))={ 0 ifr=0. (a.) (0,0) Then(0,0)(0.0) equals (b.) (0,2) (a.) -1 (c.) (1,1) (b.)0 (d.) -2,1) (c.) 1 (d.) 2 4. Let f:R2 > R be defined by 8 Let f(r.y) =2(r-»') for all (.)e R. if x#0 f(x.y) =3|x| 0 Then for all (x. y)e R elsewhere (a.).) -y.) =0 dy Then at the point (0,0) which of the following statement(s) is(are) TRUE? dx (b.) v) + yy)=0 ay (a.) f is not continuous (c.) ()- r)=0 dy (b.) f is continuous (c.) f is differentiable (d.) .)+(.)) =0 (d.) Both first order partial derivatives of f nrai Hapz Khas, Near LLT., New Delhi-110016, Ph.: (011)-26537527, Cell: 9999183434 & 9899161734, 8588844789 mdemy.com: Website: www.dipsacademv.com 188 exist question no. 2, 4, 5, 6, 7, 8

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