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• 7. Evaluate the following integrals.【題組】(a)
• 5. f(x,y) =,在(-1,1)點的所有方向導數(directional derivative) 最大值是________
• 6.=__________.
• 4. Find an equation for the line through the origin(原點) tangentto the graph of y =ln x.
• 5. Find the sum of the series or show that it diverges.
• 22.下列那些放射藥物的腦部 SPECT 檢查可用於失智症的評估？① ② ③ ④ (A)①②③ (B)②③④ (C)①②④ (D)①③④
• 6.f(x,y)=x2y2-4x2-y2共有_________個鞍點(saddle point).
• 2. (7分)Let L be the line tangent to the polar curve r(θ) = at θ = 0. Theequation of L in x and y is
• 6. (a) Give the defnition of the directional derivative of f(x, y)at (a,b) in the direction of a uni
• 2.=?
• 7.y=tanx,與x軸所夾區域繞x-軸旋轉的旋轉體體積=________
• 7. Let f :[0,3]→[0,3] be a continuous function with f(0)=0 andf(3)=3. If f is one-to-one and , then=
• 【題組】(b)Hint: for a ＞ 0,a ≠ 1.
• 28. 設a，b為實數，若方程式x4−5x3＋2x2＋ax＋b＝0有一虛根 ，則a＋b＝(A)−10(B)−12(C)−14(D)−16
• (b) Show that the directional derivative of the following func-tion exists in every direction u = (u
• 1. 請問0.1奈米等於多少公尺？(A) 10n (B) 10p (C) 100p (D) 100μ
• 3.(7分)Evaluate the improper integral by transforming it into adefinite integral of the form via an
• 8.=______
• 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