The correct option is D a=−3 and c=−10
limx→∞√x4−ax3−4x2+bx+3
−√x4+3x3+cx2−3x+d=3
limx→∞−(a+3)x3−(4+c)x2+(b+3)x+3−d√x4−ax3−4x2+bx+3+√x4+3x3+cx2−3x+d=3
As x→∞, for limit to exist, −(a+3)=0⇒a=−3
When a=−3, we have
limx→∞−(4+c)x2+(b+3)x+3−d√x4+3x3−4x2+bx+3+√x4+3x3+cx2−3x+d=3
limx→∞−(4+c)+b+3x+3−dx2√1+3x−4x2+bx3+3x4+√1+3x+cx2−3x3+dx4=3
⇒−(4+c)1+1=3
⇒c=−10 and a=−3