→ Qmmm:3Q 219.70.179.171 11/20 23:54
※ 引述《Qmmm (．．Ｑ3Ｍ．．)》之銘言：
: Find f'(x). Where f(x)=|x|^sinx and f(0) = 1.
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1.確認是否連續？
(1)x>0
sinx sinx (sinx)(lnx)
lim |x| = lim x = lim e
x->0+ x->0+ x->0+
lnx
lim ___________
x->0+ 1/ sinx
= e
1/x
lim _______________
x->0+ - cscx cotx
= e
- sinx tanx
lim _____________
x->0+ x
= e
0
= e
= 1
(2)x<0
步驟同(1)
所以，確認是連續！
2.開始微分
(1)x>0
sinx
|x| - 1
lim ____________________
x->0+ x - 1
sinx
x - 1
= lim _________________
x->0+ x - 1
(sinx)(lnx)
e - 1
= lim ____________________
x->0+ x - 1
lnx
lim ________
x->0+ 1/sinx
e - 1
= _________________________
0 - 1
0
e - 1
= ______________________
0 - 1
= 0
(2)x<0
步驟同(1)
sinx
|x| - 1
∴ f'(0) = lim ____________________ = 0
x->0 x - 1
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