Jinesh Jain posted an Question
February 08, 2022 • 00:48 am 30 points
  • IIT JAM
  • Mathematics (MA)

34. let s(x)=*+x and g(x)= x'-x for all 38. let s:(-1.1)->r xe r.if f denote the inverse function of be defined as f, then the derivative of the composite s()=

34. Let S(x)=*+X and g(x)= x'-x for all 38. Let S:(-1.1)->R xE R.If f denote the inverse function of be defined as f, then the derivative of the composite S()= for ra0 and s(0) =2. If 1-cos x function gof at the point 2 is S(x)= 2a, is the Taylor expansion of f (a)3 for all x in (-1,1), then is (b.) (a.) 0 (b.) (c.) (c.)1 (d.) 2 (d.) 39. For every function f:0. 1]R which is 35. Let f(t)=|*-25| for all xe R. The total twice differentiable and satisfies f'()21 number of pints of R at which f attains a for all xe0,1, we must have local extremum (minimum or maximum) is (a.) "() 20 for all xE[0.1] (a.) 1 (b.) f(x)2 x for all xe [0, (b.) 2 (c.) S()-h SfG)-for all ,,E0.1 (c.) 3 with x 24 (d.)4 (d.) s(x,)- 2S(z)-, for all ,E [0.1 with ,2 36. The coefficient of (xr -1) in the Taylor series expeansion of f(x) = xe" (xe R) Let f(x)= (x-2)" (r+5). Then 40. about the point x =l is (a.) f does not have a critical point at 2 (a) (b.) f has minimum at 2 (c.) fhas maximum at 2 (b.) 2e (d.) fhas neither minimum nor maximum (c.) at 2 41. Let o:R>R be a differentiable function (d.) 3e such that is strictly increasing with 37. Let a be a non-zero real number, Then '(1)=0. Let a andß denote the minimum and maximum values of o(x) on the interval 2,3, respectively. Then which one of the following is TRUE? lim- sin ()dt equals (a.)sin (a) 2a (a.) p=p(3) (b.)cos(a?) (b.) a= p(2.5) 2a (Cc.) P=p(2.5) (c.)sin (a*) 2a (d.) a = p(3) (d.) -cos (a) 186 10016 Ph.: (011)-26537527, Cell: 9999183-44 & 989916174, 8S8SS44789 aGademy-co please provide us the solutions of all the sums, sir

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