Manipal MET2012MathematicsLimits

If _ x ( x^3+1 x^2+1 -(a x+b) )=2 , then

Options

Aa=1, b=1
Ba=1, b=2
Ca=1, b=-2
DNone of these

Correct answer

C. a=1, b=-2

Step-by-step solution

aligned & _ x ( x^3+1 x^2+1 -(a x+b) )=2 & _ x x^3(1-a)-b x^2-a x+(1-b) x^2+1 =2 & _ x x(1-a)-b- a x + 1-b x^2 1+ 1 x^2 =2 & 1-a=0 and -b=2 & a=1 and b=-2 aligned

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