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Limits and Derivatives

JEE Main 2024 (Online) 29th January Evening ShiftNumericalMedium📈 Topic in 33% papers+4
Ques. 1JEE Main 2024, 29 January (Evening Shift)

Let the slope of the line 45x+5y+3=0 be 27r1+ 9r22 for some r1, r2 R. Then x 3 ( 3x 8t2 3r2x2-r2x2-r1x3-3x dt ) is equal to .

Answer

12

Solution

Slope =-9 27r1+ 9r22=-9

Let g(x)= 3r2x2-r2x2-r1x3-3x (free of t)

limit = x 3 3x8t2 dtg(x), g(3)=- (27r1+ 9r22 )-9=0 ( 00 )

L'Hôpital: = 8(3)2g'(3), g'(3)= 3r22-6r2-27r1-3=- (27r1+ 9r22 )-3=6

limit = 726=12

Answer: 12

Keep practising — Limits and Derivatives

Ques. 2JEE Main 2024, 27 January (Morning Shift)

If a= x 0 1+ 1+x4- 2x4 and b= x 0 2x 2- 1+ x, then the value of ab3 is :

  1. 36
  2. 25
  3. 32
  4. 30
Ques. 3JEE Main 2024, 27 January (Evening Shift)

If x 0 3+ x+ x+ e(1-x)3 2x= 13, then 2 - is equal to :

  1. 2
  2. 1
  3. 5
  4. 7

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