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討論串[微積] Limit 極限問題
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爆掉example. consider f(x)= 0 , x=0. (x^2)sin(1/x) , x>0. then f is differentiable at [0,+oo) (用定義做可以做0那一點). but f'(x) is not continuous at 0. Now. f(x)
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關鍵在於 c. lim f'(c(x)) = f'(xo). x→xo. "這個等號只成立在 f' is continuous at xo ". 這句話是錯的!!. 1. 例如, h:(0,∞) → |R s.t. h(x) ＝ sin(──) for all x in (0,∞).. x. 1 1
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Consider f:R→R , f is differentiable at xo , but f' is not continuous at xo. fix xo, MVT tells us. f(x)-f(xo). ───── = f'(c(x)) , where xo─c(x)─x (i.e
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改一下題目. If f(x) = g(x) for all x€(0,+∞), then. ｌｉｍ f(x) ＝ ｌｉｍ g(x). x→0+ x→0+. Proof. If ｌｉｍ f(x) = L € |R, then for any fixed ε > 0, there exists a δ
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