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February 3, 2022 11:06 am 30 pts
Ques 38 448IT-JAM: MATHEMATIcs-Previous Year Solved Paper b If f(x)g (x) is differentiable at x=c xe R satisfying 1lim e y (x)=0. Then both f and g are differentiable atx= xo lime yx)= 0 (c) f is not differentiable at x =c ht f(x) g (x) may be differentiable at y(0)10 x =c for some differentiable function g = C f and g are not differentiable at xo e) yis a bounded function on R (d) y(1)=0 but f +g may be differentiable at x=o 36. A function f (x, y) onR2 has the following 39. Let G be a finite group of order n and a e G is the only element of order 2. Then which of the following is/are trueP partial derivatives (xu)=x )- x y Then Ja) ae Z(G) f has directional derivatives in all direction everywhere (b) ae Z(G) f has a derivative at all points a is self conjugate element (c) f has directional derivative only along Jd) o(2(G)) is even the direction (1, 1) everywhere (d) f does not have directional derivatives 40 Let f: R R be defined by in any direction everywhere x (x,y) + (0,0) f(x,u) = at (0,0) 37. Let V={flf:R->R is continuously (x,u)(0,0) differentiable; and S={1,x, x, x,.. let (a) fis not continuous W=(S) be a subspace of V(R) then (b fis continuous, and both f and Jy exist (a) Every continuously differentiable le) eJf is differentiable function is member of W W Rx=a, ta,x+... +a,x" |a, e R, fand f exist but f is not differentiable neNu{o} NAT Numerical Answer Type 3 continuous functions which are not number of W Q. 41 Q.50 Carry One Mark Each Some non-differentiable functions are also number of W -1-1Sx <0 f()1: 0sxS1 41. 38 Choose the correct statement: (a) If fog is differentiable atx = c then g is A F:F (x) = f(x),xe-1,1 differentiable at cand f is differentiable then A= at g(c) 637627
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• Navdeep goyal 1
39 