課程名稱︰微積分甲上
課程性質︰系內必帶
課程教師︰陳宏
開課學院：工學院
開課系所︰土木工程學系
考試日期（年月日）︰2009/10/27
考試時限（分鐘）：50min
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
Make sure to give sufficient reason in each problem or you will NOT get any
credit for your answer.
1. (20 points) Let
L(x)=sin((x+2)^(3/4))-sin(x^(3/4))
Evaluate the limit of L(x) as x goes to infinity.
Solution: Refer to Q4 of 95 midterm.
http://www.math.ntu.edu.tw/~mathcal/download/exam/951cala1_midso1.pdf
2. (20 points) Given the curve x(y)^(2)+x+y=3, find dy/dx and (d)^(2)y/d(x)^(2)
at the point (1,1)
Solution: Refer to Q3 of 94 midterm.
http://www.math.ntu.edu.tw/~mathcal/download/exam/941cala_2mid.pdf
3. (20 points) Using a linear approximation to estimate the value cot46(deg).
Is your approximation accurate to within 0.1?
Solution: Refer to Q5 of 94 midterm.
http://www.math.ntu.edu.tw/~mathcal/download/exam/941cala_2mid.pdf
4. (20 points) Evaluate the following limit
1
lim x(√(x^2-x)-x)sin---
x→∞ x
Solution: Refer to Q1(a) of 94 midterm.
http://www.math.ntu.edu.tw/~mathcal/download/exam/941cala_1mid.pdf
5. (20 points) Find dy/dx where y=(Inx)^(x/2) on y>1
Solution: Refer to Q2(b) of 96 midterm.
http://www.math.ntu.edu.tw/~mathcal/download/exam/961A2m.pdf
※ 此小考全從歷屆考古提出
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 118.168.91.248