The value of limx→−∞ x2−x+1+x, is

We have,limx→−∞ x2−x+1+x =limy→∞ y2+y+1−y, where y=−x=limy→∞ y2+y+1−yy2+y+1+yy2+y+1+y=limy→∞ y2+y+1−y2y2+y+1+y=limy→∞ y+1y2+y+1+y=limy→∞ 1+1y1+1y+1y2+1=12ALITER    limx→−∞ x2−x+1+x=limx→−∞ x2−x+1+xx2−x+1−xx2−x+1+x=limx→−∞ x2−x+1−x2x2−x+1−x=limx→−∞ −x+1x2−x+1−x=limx→−∞ −x|x|+1|x|x2−x+1|x|−x|x|             [ Dividing Nr and O' by x]=limx→−∞ −x−x −1xx2x2−x2+1x2+xx∵x2=|x|=−x as x<0=limx→−∞ 1−1x1−1x+1x2+1=12