求：lim x->负无穷 x(sqr(x^2+100)+x)

优质解答

原式=lim x->负无穷[-(- x)(sqr(x^2+100)+x)(sqr(x^2+100)-x)]/(sqr(x^2+100)-x)
=lim x->负无穷[-(- x)((x^2+100)-x^2)]/(sqr(x^2+100)-x)
=100lim x->负无穷[-(- x)]/(sqr(x^2+100)-x)
=100lim x->负无穷[-1]/(sqr(1+100/x^2)+1)
=100×（-1）/(1+1)
=-50 原式=lim x->负无穷[-(- x)(sqr(x^2+100)+x)(sqr(x^2+100)-x)]/(sqr(x^2+100)-x)
=lim x->负无穷[-(- x)((x^2+100)-x^2)]/(sqr(x^2+100)-x)
=100lim x->负无穷[-(- x)]/(sqr(x^2+100)-x)
=100lim x->负无穷[-1]/(sqr(1+100/x^2)+1)
=100×（-1）/(1+1)
=-50