Re: [考古] 91嘉大
※ 引述《kuovsphy (反駁無罪 嗆人有理)》之銘言：
: 2 f(x+h)+f(x-h)-2f(x)
: 10.令f(x)=sin x，則 lim－－－－－－－－－－=
: h→0 2
: h
: 第二題怎麼解原式的分母就會有x很困擾
: 第10題分母是h的平方耶
: 先謝謝板上微積分高手囉
f(t+a) = f(t) + f'(t)a + f''(c)/2! a^2, c some number between t+a and t
f(x+h) + f(x-h) - 2f(x)
-----------------------
h^2
[f(x+h)-f(x)] + [f(x-h)-f(x)]
= -----------------------------
h^2
[f'(x)h + f''(ξ)/2! h^2] + [f'(x)(-h) + f''(η)/2! (-h)^2]
= -----------------------------------------------------------
h^2
= (f''(ξ) + f''(η))/2
f''連續; ξ,η-> x 當 h -> 0
原式趨近 f''(x)
希望沒錯><
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