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Manipal MET2014MathematicsLimits

_ x 2 (1- x 2 )(1- x) (1+ x 2 )( -2 x)^3 is equal to

Options

  1. A1 8
  2. B0
  3. C1 32

Correct answer

C. 1 32

Step-by-step solution

Put x= 2 -h as x 2 , h 0 aligned & Given, limit = _ h 0 1- ( 4 + h 2 )(1- h) 1+ ( 4 + h 2 )(2 h)^3 & = _ h 0 ( h 2 ) _ h 0 2 ^2 ( h 2 ) 8 h^3 & = _ h 0 1 4 ( h 2 2 h 2 ) _ h 0 ( h 2 h 2 )^2 1 4 & & = 1 32 aligned

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