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• 7. (10 points) Determine and classify the stationary points of the function f(x,y)=xy(3x+6y-2).
• 8. (10 points) Find the total arc length of the cardioid r = a(1-cosθ),a＞0.
• (E). Let g(x) be the inverse function of the strictly increasing function f(x) =x5 + 3x3 + 1. Theng(
• (c) Show that the above function f(x, y) is not differentiableat (0,0)
• 8. The radius of convergence of the power series is___________.
• 8. Find the following limits.【題組】(a)
• 9. (10 points) Use change of variablesto evaluate the integral , where
• 7. Use the transformation z = u/v, y = v to evaluate the doubleintegralwhere R is the region in the
• 9.銀行年利率為 1%,若存進10萬元,以月計算複利,大約_______年後存款會變成40萬元(在個位數四捨五入,差距在2年内都算對)
• 1. Let f:R→R be twice differentiable. If f" is nowherevanishing, then f has at most two distinc
• (F). The coefficient of x9 in the Taylor expansion of fo dt is________.
• 29. 橢圓Γ： 上任一點P，到直線L：x−2y＋15＝0的距離之最小值為(A) (B) (C) (D)
• 10.(本大题請標出底下各小前的編號)f(x)=,回答下列問題,並作圖:【題組】(1)此函數圖形遞減凹向下(convace down)的範圍在________
• 2. Prove that
• 1. 小明欲配製0.5M的碳酸鈉溶液1升，則其配製的方法，下列何者正確？(碳酸鈉分子量為106)(A)將53克的碳酸鈉溶入1升的水中(B)將106克碳酸鈉溶於水中，並定量至1升(C)將106克的碳酸鈉
• 【題組】(2)此函數形是否有漸近線?若有,請寫出漸近線方程式:_______
• 【題組】(3)請在答案本作y=f(x)的略圖。
• 4.(7分)Evaluate dx=_____.
• 11.計算題:求
• 9. Show that
• 3. Evaluatedy,where C is the unit circle.
• 23.下列核醫製劑何者不適合用於心肌灌流造影？(A) (B) (C) (D)
• 5. (8分)Let p(x)=x6+2x5-x+1. Find =_________·
• 1. 依自來水法，供水區域涉及三個行政區域之自來水事業，下列何者為其主管機關？(A)行政區域中最大者 (B)預算編列最多者(C)行政人員最多者 (D)上一級之主管機關
• 10 Consider the funetion f(x,y) = ax2 + βy2. Find values for a and β so that (a) (0,0) isa local min