微积分题，如图
展开全部
|a+xb|^2
=(a+xb).(a+xb)
=|a|^2+2x(a.b) + x^2.|b|^2
/
lim(x->0) ( |a+xb| - |a| )/x
=lim(x->0) ( |a+xb|^2 - |a|^2 )/[ x ( |a+xb| + |a| ) ]
=lim(x->0) ( 2x(a.b) + x^2.|b|^2 )/[ x ( |a+xb| + |a| ) ]
=lim(x->0) ( 2(a.b) + x|b|^2 )/[ ( |a+xb| + |a| ) ]
=(a.b) /|a|
=(a+xb).(a+xb)
=|a|^2+2x(a.b) + x^2.|b|^2
/
lim(x->0) ( |a+xb| - |a| )/x
=lim(x->0) ( |a+xb|^2 - |a|^2 )/[ x ( |a+xb| + |a| ) ]
=lim(x->0) ( 2x(a.b) + x^2.|b|^2 )/[ x ( |a+xb| + |a| ) ]
=lim(x->0) ( 2(a.b) + x|b|^2 )/[ ( |a+xb| + |a| ) ]
=(a.b) /|a|
本回答由提问者推荐
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
