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Limits and Derivatives · Question 4

JEE Advanced 2024 Paper 2Multiple CorrectHard📈 Topic in 17% papers+4−1
1

Let S be the set of all ( , ) R R such that x (x2)( e x) ( 1x2 )x ( e(1+x)) =0. Then which of the following is (are) correct?

  1. (-1,3) S
  2. (-1,1) S
  3. (1,-1) S
  4. (1,-2) S

Answer

(2) (-1,1) S, (3) (1,-1) S

Solution

As x : 1x2 1x2, e(1+x) e x, and (x2) oscillates in [-1,1].

Expression (x2) ( e x) - x-(2+ ).

It tends to 0 iff 2+ >0, or 2+ =0 with - <0.

(A) =-3: x1 grows, no. (B) =-1: x-1 0, yes. (C) =-1: yes. (D) =-2, - =3>0: ( x)3 (x2) does not tend to 0, no.

Answer: (B), (C)

JEE Advanced 2024 Paper 2

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