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Question

If limx(x4ax34x2+bx+3x4+3x3+cx23x+d)=3, then
  1. a=9 and c=3
  2. a=3 and c=10
  3. a=2 and c=0
  4. a=3 and c=10


Solution

The correct option is B a=3 and c=10
limxx4ax34x2+bx+3
x4+3x3+cx23x+d=3

limx(a+3)x3(4+c)x2+(b+3)x+3dx4ax34x2+bx+3+x4+3x3+cx23x+d=3
As x, for limit to exist, (a+3)=0a=3
When a=3, we have
limx(4+c)x2+(b+3)x+3dx4+3x34x2+bx+3+x4+3x3+cx23x+d=3

limx(4+c)+b+3x+3dx21+3x4x2+bx3+3x4+1+3x+cx23x3+dx4=3

(4+c)1+1=3
c=10 and a=3

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