数学Paper 1讨论专区

hongji

[2x(x^2 + 3) ]/ [ (x^2  -1)^3 ]  >  0

这个graph 怎样画？可以教我吗？谢谢

menglee90

回复 2719# hongji


     

menglee90

回复 2721# hongji

> 0 ? 还是 = 0？是要找x 的range?

hongji

given a curve y= x^2  -  4 and a straight line y=x - 2


(a) calculate the area of the region R bounded by the curve and the straight line.



(b)find the volume of the solid formed when R is rotatd through 360 (degree) about the x-xis.

hongji

回复  hongji

> 0 ? 还是 = 0？是要找x 的range?
menglee90 发表于 28-7-2011 10:27 AM

    > 0 ...


yes ,find x range and sketch ...

menglee90

回复 2721# hongji


   我只帮你找x的range。

[2x(x^2 + 3) ]/ [ (x^2  -1)^3 ]  >  0

Since (x^2 + 3) always > 0 , we only consider 2x/ (x^2  -1)^3
2x/ (x^2  -1)^3 > 0 when 2x and (x^2  -1)^3 are both positive or both negative, x =/= 1, -1


Case 1:
2x>0                    and           (x^2  -1)^3 > 0
x>0                                         (x^2  -1) > 0
                                               x<-1 , x>1
Therefore, x>1


Case 2:
2x<0                    and           (x^2  -1)^3 < 0
x<0                                         (x^2  -1) < 0
                                                  -1<x<1
Therefore, -1<x<0


Combining two cases, x>1 and -1<x<0

menglee90

回复 2724# hongji


   提示：把graph画出来，找line和curve的intersection point，就知道integrate的limits了。

huatiang

回复 2669# peaceboy

Thank you

hongji

我想问，
1/2 In 2 + In2

怎样加起来等于3/2 In 2 ...

woeifang

回复 2729# hongji


和平常做algebra的方法一樣

如:  x+2x=3x
       3ln2+2ln2=5ln2

       x+(1/2)x=(3/2)x
       ln2+(1/2)ln2=(3/2)ln2

Allmaths

我想问，
1/2 In 2 + In2

怎样加起来等于3/2 In 2 ...
hongji 发表于 9-8-2011 08:02 PM

    不然就factorize ln 2出来就可以了。。

(1/2)ln 2+ln 2=[(1/2)+1]ln 2
                      =(3/2)ln 2

hongji

我想问sketch the graph f(x) =（ [4^ekt]  +  1 ） / （[4^ekt]   -  1 ）
when k are constant

怎样画TT

badkids91

哪一个软件可以帮我们画graph并且可以列出intersection point,max point,min point,inflection pt,roots等等的?

menglee90

回复 2733# badkids91

可以试试wolframalpha.com
例子：plot x^2+4x+7, 2x+4

Log

我想问sketch the graph f(x) =（ [4^ekt]  +  1 ） / （[4^ekt]   -  1 ）
when k are constant

怎样画 ...
hongji 发表于 11-8-2011 02:41 PM

4^ekt 还是 4e^kt...??

hongji

4^ekt 还是 4e^kt...??
Log 发表于 15-8-2011 10:57 AM

是4e^kt.
   ，我写错了

hongji

5.A variable point P lies on the line x = -4 and O is the origin.A straight line which is parallel to the x-axis and passes through the point P meets the straight line which passes through the origin O and perpendicular to OP at Q. Show that the locus of Q is [y^2] = 4x.

6.A straight line y = m(x - 2)which passes through a fixed point (2,0) meets the lines x = 1 and y = k at A and B respectively.If O is the origin and P is the point (1,0), find the equations of lines OA and PB. If m varies,find the equations of the locus of the point of intersection between lines OA and PB.

这题我找到equation of line OA and PB 但是找不到 equation of the locus of the point of intersection

Allmaths

5.A variable point P lies on the line x = -4 and O is the origin.A straight line which is parallel t ...
hongji 发表于 27-8-2011 03:14 PM

5)  Let P(-4 , a)

Gradient of straight line OP=(a-0)/(-4-0)
                                               = -a/4

Gradient of straight line OQ, (-a/4)M2=-1
                                                          M2=4/a

Equation of straight line OQ, y=(4/a)x

When y=a, a=(4/a)x
                   x=(a^2)/4

Coordinate of Q (a^2/4 , a)

Equation of locus Q:

x=(a^2)/4           ,          y=a
x=y^2/4
y^2=4x   (shown)

Allmaths

5.A variable point P lies on the line x = -4 and O is the origin.A straight line which is parallel t ...
hongji 发表于 27-8-2011 03:14 PM

Equate equation of straight line OA和PB来找到intesection point。

然后就用parametric来找equation of locus。

hongji

Equate equation of straight line OA和PB来找到intesection point。

然后就用parametric来找equa ...
Allmaths 发表于 27-8-2011 06:28 PM

如果math paper2 可以A,math paper 1 最少要拿多少能A & B?