JEE Advanced2012MathematicsLimitsActual

If _ x ( x²+x+1 x+1 -a x-b )=4 , then

Options

Aa=1, b=4
Ba=1, b=-4
Ca=2, b=-3
Da=2, b=3

Correct answer

B. a=1, b=-4

Step-by-step solution

Given: _ x ( x²+x+1 x+1 -a x-b )=4 array l _ x x²+x+1-a x²-a x-b x-b x+1 =4 _ x (1-a) x²+(1-a-b) x+(1-b) x+1 =4 array For this limit to be finite 1-a=0 a=1 then given limit reduces to _ x -b x+(1-b) x+1 =4 _ x -b+ (1-b) x 1+ 1 x =4 -b=4 or b=-4, a=1, b=-4

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