Question

求这两道打勾的高数题的详细解答过程，谢谢

Answer 1

(3) 解：
lim((x,y)→(0,0))[2-√(xy+4)]/(xy)
=lim(u→0)[2-√(u+4)]/u (u=xy)
=lim(u→0){[2-√(u+4)][2+√(u+4)]}
/{u[2+√(u+4)]}
=lim(u→0)[4-(u+4)]/{u[2+√(u+4)]}
=-lim(u→0)1/[2+√(u+4)]
=-1/[2+√(0+4)]
=-1/4；
(5) 解：
lim((x,y)→(2,0))[tan(xy)]/y
=lim((x,y)→(2,0)){x·[tan(xy)]/(xy)}
=lim((x,y)→(2,0))x
·lim((x,y)→(2,0))[tan(xy)]/(xy)
=2·lim(u→0)(tanu)/u (u=xy)
=2·1
=2.