Re: [微積] 有幾題微積分題目想問大家

看板Math作者rachel5566 (rachel5566)時間15年前 (2011/02/19 13:27)推噓2(2推 0噓 2→)

留言4則, 4人參與討論串2/2 (看更多)

※ 引述《plc123 (荷包蛋)》之銘言： : 非常的抱歉我是用pdf檔的方式呈現，所以須先下載 : http://www.badongo.com/file/25110356 回答前兩題... 1. f(x) = (2^x+5)/(2^x-1) 反函數整理 ======> x = (2^y+5)/(2^y-1) ====> y = f^(-1)(x) = log [(x+5)/(x-1)] 2 => [f^(-1)]'(x) = (1/ln2)(ln[(x+5)/(x-1)])' = -6/[(ln2)(x+5)(x-1)] => [f^(-1)]'(3) = -3/(8ln2) 2. x = 4 = t^3-2t => t = 2 dy/dt = 2(f(x)+3x)[(df/dx)(dx/dt)+3(dx/dt)] = 2(f(t^3-2t)+3t^3-6t)[f'(x)(3t^2-2)+3(3t^2-2)] (dy/dt)|t=2 = 2(f(4)+3*4)(f'(4)*10+3*10) = 2*15*10(f'(4)+3) = 150 => f'(4) + 3 = 1/2 => f'(4) = -5/2 剩下三題題目是: (下次要問問題有誠意點把題目打上來，便當狗很難用咧...) 3. lim [x+√(x^2+ax)] = b，b≠0，求b/a=? x→∞ 4. 如果 lim [(3-2kx)/(5+2kx)]^(4x) = 10，求k x→∞ 5. f(x) = x^3-|1-3x^3|，xε[-2,3]，求f在[-2,3]的最大值 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.211.87

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Indigoa

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plc123

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Rasin

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