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MHT CET202416 May 2024Evening ShiftMathematicsContinuity and DifferentiabilityActual

If the function f defined on ( 6 , 3 ) by f(x)= array cc 2 x-1 x-1 , & x 4 k , & x= 4 array . is continuous, then k is equal to

Options

  1. A1 2
  2. B2
  3. C1
  4. D1 2

Correct answer

A. 1 2

Step-by-step solution

f (x) is continuous on ( 6 , 3 ) . f (x) is continuous at x= 4 . f ( 4 )= _ x 4 2 x-1 x-1 Applying L'Hospital's rule on R.H.S., we get aligned f ( 4 ) & = _ x 4 2 (- x) - cosec ^2 x & = 2 4 cosec ^2 4 & = 2 ( 1 2 ) ( 2 )^2 & = 1 2 aligned

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