作者justalone101 (ㄚ挺)
看板Math
标题[微积] 一些微积分相关问题
时间Sun Jan 9 15:00:13 2011
1. f(x)=lnx/x on (0,∞)
(a) Find critical points, the intervals where f(x)increases , decrease
(b) Find the extreme values
(c) Determine the concavity of the graph and find the points of inflection
2. Given x+1=0 and x+y^2=0
(a) Find the area of the bounded region determined by the above two curves
(b) Locate the centroid of the bounded region
(c) Find the volume of the solid generated by revolving the bounded region about the y-axis
3.
(a) Let f(x)= (ax+b)/(cx+d) with x≠ -d/c Show that f is one-to-one if ad-bc≠0
4.
∫ cscx dx = ∫ sinx/(1-cos^2x) dx
Show that ∫ cscx dx= ln√(1-cosx)/(1+cosx) +C
麻烦各位大大帮我解答 可以的话 解法可以站内信给我 谢谢!!
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1F：→ suker :4sinx/(1-cos^2x) =(sinx)/2(1-cosx)+sinx/2(1+cosx) 01/09 15:07
2F：→ suker :4. (1/2)ln (1-cosx) -(1/2) ln (1+cosx) 01/09 15:07
3F：→ suker :在合并一下 就得到 ln√[(1-cosx)/(1+cosx)] +C 01/09 15:08