九十三學年度日間部轉學生招生入學考試試題紙 - CHUR

中 華 大 學

九十三學年度日間部轉學生招生入學考試試題紙

系別：電機工程學系 二年級 科目：微積分 共一頁第一頁

填空題：請按題號順序只將答案寫在答案卷第一頁，每題十分，計算過程不計分 1. sin²(ln(x))=

dx d

2. tan(arcsin(a))= 3. (x^lnx)=

dx d

4. Please write the domain and range of arcsin(x)

5. Please write the first two nonzero terms of the Taylor series of tan(x)

6. Let the power series solution of the differential equation x y x dx

y

d²₂ + ² = be

represented in the form y=a₀ +a₁x+a₂x² +a₃x³ +ΛΛ . Find this solution.

7. Use the binomial series to find a power series for the function

3 2

8 ) 1 (

x x

f = − and

its radius of convergence. Please list the first three terms of the series and its radius of convergence.

8. Find the average value of the function f(x)=e^−xsin(πx) for x∈[ 0,1].

9. =

−

−

+

− +

∫

0^1x −^x_x3 _x^x2 ^{x dx} 2

3 4

4 8 10

3

10.

∫

0 ^{/2 x 4xdx =}

2 cos

π sin