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課程名稱︰微積分甲上
課程性質︰
課程教師︰黃漢水
開課系所︰生機、生工、地質、地理、工管等系
考試時間︰94/11/21
試題 :
一.
(1)lim(√(1/t+6) － 1/3)/t^2－9
t-->3
(2)lim√(x^2+6x+2) － √(x^2+x-1)
x-->-無限
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 絕對值sin u - sin v <= 絕對值 u-v
[Hint:use mean value theorem]
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