Limits questions PLEASE HELP

2013-04-13 8:10 pm

1. lim sinx/(y-x)
x->y
2. lim 1-cosx/(x^2)
x->0
3. lim sin5x-sin3x/(sin2x)
x->0
4. lim e^x + e^-x -2/ xsin4x
x->0

回答 (1)

螞蟻雄兵

2013-04-14 2:09 am

✔ 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

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