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标题[转录][试题] 94 黄汉水 微积分甲上期中考
时间Sun Oct 21 20:23:44 2007
※ [本文转录自 NTU-Exam 看板]
作者: swl766 (阿轩 ∩__∩y ) 看板: NTU-Exam
标题: [试题] 94 黄汉水 微积分甲上期中考
时间: Tue Nov 22 19:15:48 2005
课程名称︰微积分甲上
课程性质︰
课程教师︰黄汉水
开课系所︰生机、生工、地质、地理、工管等系
考试时间︰94/11/21
试题 :
一.
(1)lim(√(1/t+6) － 1/3)/t^2－9
t-->3
(2)lim√(x^2+6x+2) － √(x^2+x-1)
x-->-无限
二.
(1)Sketch the graph of the function f(x)=三次√x^2 + 4/三次√x
(2)Find the absolutely maximum value & the absolutely minimum value of f(x)
on the interval[1,10]
三.
Find the shortest distance from the point (-8,0) to the curve y=x^2+2x+3
四.
Let f(x)=x^3-2x+1 Find all tangent lines from the point (2/3,-1/3) to the
curve y=f(x)
五.
Let f(x)=x + 1/(1+x) Let L be the tangent line of f(x) at the point(a,f(a))
,where a>1 Find the area of the triangle bounded by the lines L,y=x,&x=1
六.
Let u,v be two real numbers
Prove that 绝对值sin u - sin v <= 绝对值 u-v
[Hint:use mean value theorem]
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1F：推 alex1025:怎麽跟统一命题差那麽多 11/23 19:48
※ jenny83131:转录至看板 NTUGEO95-HW 12/02 01:16
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2F：推 hsj8266:感谢! 10/22 02:17