✔ 最佳答案
1. lim(x->y)_Sinx/(y-x)
Sol
lim(x->y)_Sinx/(y-x) 0/0type
=lim(x->y)_Cosx/(-1)
=-Cosy
2. lim(x->0)_[(1-Cosx)/x^2]
Sol
lim(x->0)_[(1-Cosx)/x^2] 0/0 type
=lim(x->0)_Sinx/(2x) 0/0 type
=lim(x->0)_Cosx/2
=1/2
3. lim(x->0)_[(Sin5x-Sin3x)/Sin2x]
Sol
lim(x->0)_[(Sin5x-Sin3x)/Sin2x] 0/0 type
=lim(x->0)_[(5Cos5x-3Cos3x)/(2Cos2x)]
=(5-3)/2
=1
4. lim(x->0)_(e^x + e^-x -2)/(xSin4x)
Sol
lim(x->0)_(e^x + e^-x -2)/(xSin4x) 0/0 type
=lim(x->0)_{[e^x-e^(-x)]/(4xCos4x+Sin4x) 0/0 type
=lim(x->0)_{[e^x+e^(-x)]/(-16xsSin4x+4Ccos4x+4Ccos4x)
=2/8
=1/4