作者andy0130tw (Andy Pan)
看板DoubleMajor
标题[试题] 104资工转系考 微积分
时间Wed Jul 20 00:41:31 2016
题号可能有错，还请各位大大帮忙修正><
1. Write down the definition of The Fundemental Theorem of Calculus.
sin x^4
2. (a) lim --------- = ?
x→∞ sin^4 x
cot x
(b) lim (1+x) = ?
x→0+
-1
3. (a) ∫sin (2x) dx = ?
x^2 + 3x + 2
(b) ∫-------------- dx = ?
3x (x^2 + 2)
(3n)! x^n
4. Find the interval of convergence of Σ -----------.
x→∞ n^(3n)
5. Solve the initial value problem dy/dx = sqrt(4-y^2), y(π/3) = 1.
2 2
6. Find and classify the critial points of f(x,y) = x + ?? + xy + ??.
(忘记方程式了)
2 2 2 2
7. Find the points on the intersection of 3x + y = 2 and x + 2y + z = 3
that are closet and furthest from the origin.
(不确定方程式)
2x - y
8. ∫∫ sin (--------) dA, where R is enclosed by 1 ≦ 2x + y ≦ 2,
R 2x + y
2x - y = 0 and 2x + 5y = 0.
2 √x 2 3
9. f(x) - x = ∫ f(t )t dt. Find f(x).
1
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1F：推 j6cl3: 推 好像有点难@@ 07/20 00:44
2F：推 dsamylife: 搂主真强者 07/20 00:52
3F：推 wrytus: 楼主超强提早写完还有时间慢慢来背题目 07/20 12:51
※ 编辑: andy0130tw (180.218.144.207), 07/24/2016 22:21:59
4F：→ eopXD: 第四题应该是 n 趋近无限才对 07/13 16:01
5F：→ eopXD: 乾 想错@@ 07/13 16:12