高数limx趋于负无穷x[(x^2+10)^1/2+x]=?
2019-06-02
高数limx趋于负无穷x[(x^2+10)^1/2+x]=?
优质解答
=lim x(x^2+10-x^2)/[(x^2+10)^1/2 - x]
=10 * lim x/[-x(1+10/x^2)^1/2 - x]
=10 * lim 1/[-(1+10/x^2)^1/2 - 1]
=10 * 1/[-(1+0)^1/2 - 1]
=-10 * 1/2
=-5
=lim x(x^2+10-x^2)/[(x^2+10)^1/2 - x]
=10 * lim x/[-x(1+10/x^2)^1/2 - x]
=10 * lim 1/[-(1+10/x^2)^1/2 - 1]
=10 * 1/[-(1+0)^1/2 - 1]
=-10 * 1/2
=-5