milk>試卷(2021/08/26)

# 110 年 - 110 國立臺灣大學_碩士班招生考試_部分系所:微積分(B)#100708

【非選題】
1.1.Sketch the figure of function (x3-1)/x and indicate the extrerna, inflection points, and concavity. (20%)

【非選題】
2.

2.Calculate the given integral.(a)(b)；(c).(15%)

【非選題】
3.

3. State whether the sequence converges as n→∞； if it does, find the limit. (a) (b) (10%)

【非選題】
4.

4. Find the unit tangent, the principal normal, the curvature and wite an equation in x, y, z for the osculating plane at the point on the curve at t=0 and find the length from t=0 to t=ln3. (15%)

【非選題】
5.5. Expand sin(x) in powers of x-t and specify the values of x for which the expansion is valid. (10%)

【非選題】
6.

6. Let and S be the lower half of the ellipsoid.. Calculate the flux ofin the direction of the upper unit normal. (15%)

【非選題】
7.

7. Take S as the parallelogram bounded by x + y= 0,x+y= 1, x -y=0,x -y= 2. Evaluate .(15%)

### 懸賞詳解

#### 國三數學上第一次

1.( )已知 x：y＝3：4，x：z＝4：1，則 x：y：z ＝？ (A) 3：4：1 (B) 12：4：1 (C) 12：16：3 (D) 12: 16：1。...