pure maths

Let x=y+h
lim (x->y) (x^9-y^9)/(x^5-y^5)
=lim (h->0) [(y+h)^9-y^9)/[(y+h)^5-y^5]
=lim (h->0) [(y^9+9y^8h+36y^7h^2+...-y^9)/[y^5+5y^4h+10y^3h^2+...-y^5]
=lim (h->0) [(9y^8h+36y^7h^2+...)/[5y^4h+10y^3h^2+...]
=lim (h->0) [(9y^8+36y^7h+...)/[5y^4+10y^3h+...]
=(9/5)y^4

Using L'Hospitals' rule
lim (x->y) (x^9-y^9)/(x^5-y^5)
=lim (x->y) (9x^8)/(5x^4)
=(9/5)y^4

2010-04-15 14:10:25 補充：
OK