[微積] 幾題概念
1.Which of the following statements are wrong for the real function
f(x) on (a,b)?
If f(x) is continuous on (a,b),thenf(x)has an absolute minimum on
(a,b).
反例是水平線?
2.Consider f(x)={x^2sin(1/x^3) ifx>0, 0 ifx<_0},
which of the following statement are true?
(A)f is continuous on {R} (B)f is differentiable on {R}
(C)f'(0)=0 (D)f' is continuous on{R}
答案ABC 我不會的是(D) 我是把f"(x) (x>0時)算出
再看它是不是在正實數中都有定義 因f'可微的話必連續
我這樣想法有錯嗎? 能否把其他選項的作法講一下 稍微確認~
3.Let f(x) be a real function such that f"'(x)exists for all real numbers
Which of the following are the right expression of f"(x)?
(A)f"(x)=lim(h->0) f(x+h)+f(x-h)-2f(x)/h^2
(C)f"(x)=lim(h->0) f'(x+h)+f'(x-h)-2f(x)/2h
(D)f"(x)=lim(h->0) f'(x+h)-f'(x-h)/2h
答案AD 可是我寫AC 已知A對後用L'Hospital 得C.....
不知道為什麼錯...順便問一下(A)的算法.
感謝花時間看完我問題m(_ _)m
跪求幫忙!!
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