JEE Main2014MathematicsLimitsActual

If _ x 2 (x-2 x^2+k+2 x-2 k . x^2-4 x+4 =5 , then k is equal to:

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D. 3

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aligned & _ x 2 (x-2) x^2+(k-2) x-2 k x^2-4 x+4 =5 & _ x 2 (x-2) x^2+k x-2 x-2 k (x-2)^2 =5 & _ x 2 (x-2) x(x-2)+k(x-2) (x-2) (x-2) =5 _ x 2 ( (x-2) (x-2) ) _ x 2 ( (k+x)(x-2) (x-2) )=5 & 1 _ x 2 (k+x)=5 & _ h 0 h h =1 & or k+2=5 k=3 aligned

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