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6.=__________.
問題詳情
6.
=__________.
參考答案
上一篇 :
5. f(x,y) =,在(-1,1)點的所有方向導數(directional derivative) 最大值是________
下一篇 :
4. Find an equation for the line through the origin(原點) tangentto the graph of y =ln x.
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5. Find the sum of the series or show that it diverges.
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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(
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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________.