→ Alip:你的ip好妙.... 01/25 22:59
→ goshfju:@@? 01/26 01:06
推 FantasyNova:可能是台大的IP吧 01/26 01:17
→ goshfju:我在家裡啊 XD 01/26 01:41
推 nisrok:140.112.xx.xx才是台大的 01/26 07:22
推 bko2439:推文可以轉笨版了XD 01/26 20:58
上學期期中考
1.(15%)Find the indicated limit
2|x-1|-x+1
(a) lim -------------
x→1 2|x-1|+x-1
[1/x]
(b) lim x(-1) where [ ] is the greatest integer function
x→0
1-cosθ
sin(--------)
θ
(c) lim -----------------
θ→0 θ
2.(10%)Use the ε-δ definition of a limit, prove that
lim √(x+1) = 2
x→3
3.(10%)Give an example to show that the following is false:
If lim f(x)=L and lim g(x)=M then lim g(f(x))=M
x→a x→L x→a
4.(10%)Give an arbitrary number c, show that the equation x+sinc=c
always has a solution
5.(25%)(a)Discuss the continuity and differentiable at x=0 for
the following functions f(x) and g(x),
1 2 1
f(x)= sin--- , x≠0 g(x)= x sin--- , x≠0
x x
and
= 0 , x=0 = 0 , x=0
xcosx
(b)Let f(x)=tan√(-----------) , where a is a constant
a^2+x^2
find f'(x)
6.(10%)Use the Mean Value Theorem to show that
√(1+x) < 1+0.5x
3 2
7.(10%)Find a cubic function f(x)=ax +bx +cx+d that has a local maximum
value 3 at -2 and a local minimum value 0 at 1
8.(10%)Find all equations of asymptotes of the graphs of
4x^2-2x+5
y=-------------
2x^2+x-3
9.(10%)Assume
s''(t)=10sint+3cost, s(0)=0, s(2π)=12
Find s(t)
x^2 y^2
10.(16%)Given the ellipse E: ----- + ----- = 1
a^2 b^2
(a) Show by implicit differentiation that the tangent
line to E at the point (Xo,Yo) is
Xo*x Yo*y
------- + ------- =1
a^2 b^2
(b) Find the area of the largest rectangle that be
inscribed in E
喔..沒期末考的考卷
但是期末考總分有150喔!
分數是依照小考*25% 作業*5% 期中*35% 期末*40%算的
但其實期末考破百的人不少喔..也就是說後面那個40很多人都拿到破40的分數喔
所以說再加上作業的5%....學期成績大約是用130分去扣的..蠻容易拿高分的@@"
期末考佔非常重..但我覺得期末考的題目比期中簡單
期末幾乎都是偏計算的題目...積分積得出來就好啦
不像期中有些證明..有些又要求從基本定義下手
我是雙修生..雖然以前就修過微積分了..但還是又要再修一次@@""
但也因為這樣..這學期靠這科賺了不少分數喔!
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