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AP EAMCET201922 Apr 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

Given, ( x= _ n=1 ^ (-1)^ n-1 x^ 2 n-1 (2 n-1) ! ). If the function (f(x) ) given by (f(x)= ( x)- x x^4 (x 0) ) and (f(0)=k ), is continuous at (x=0 ), then (k= )

Options

  1. A( 1 6 )
  2. B( 1 3 )
  3. C( 1 2 )
  4. D0

Correct answer

A. ( 1 6 )

Step-by-step solution

Given, ( aligned f(x) & = ( x)- x x^4 & = _ x 0 2 ( x+x 2 ) ( x- x 2 ) x^4 & = _ x 0 2 (x) ( x^3 12 ) x x^3 12 12 [ Applying x=x- x^3 3 ! + ] & = _ x 0 2 ( x x ) ( x^3 12 ) ( x^3 12 ) 1 12 =2 1 1 1 12 = 1 6 aligned )

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