数学Paper 1讨论专区

Lov瑜瑜4ever

和我的方法一样么？好奇下有没有其他解法...
peaceboy 发表于 11-8-2010 11:18 PM

不一样哦。。。
我的方法是
n^2+1
=(2k+1)^2+1 , 2k+1永远是单数,k is Natural Number
=4k^2+4k+1+1
=4k^2+4k+2
=2(2k^2+2k+1)
因为2k^2+2k+1是单数
所以n^2+1的数目最多只能被2整除

Lov瑜瑜4ever

我的意思是n^2+1的最多只能被2整除
而不能被2个factor 2连续整除...

peaceboy

我的意思是n^2+1的最多只能被2整除
而不能被2个factor 2连续整除...
Lov瑜瑜4ever 发表于 12-8-2010 06:40 PM

    比我的容易得多...

Log

白羊
dy/dx= cos 2y
∫ 1/cos 2y dy = ∫ dx
∫ sec 2y (1) dy = ∫ dx
∫ sec2y (sec 2y +tan 2y)/(sec 2y +tan 2y) dy = ∫ dx
1/2∫ (2sec² 2y +2sec 2y tan 2y)/(sec 2y +tan 2y) dy =∫ dx
1/2 ln l sec 2y + tan 2y l  = x + c
      sec 2y + tan 2y = Ae^2x ,    A=e^x
      (1+ tan y)/(1- tany) =Ae^2x
rearrange,    tan y = (Ae^2x -1)/(Ae^2x +1)
                     y = tan^-1  { (Ae^2x -1)/(Ae^2x +1) }

sec 2y + tan 2y = 1+ tan y /1- tan y can be xpress try on ur own .
u can also use substitution t= tan y for∫ sec 2y dy.

Allmaths

白羊
dy/dx= cos 2y
∫ 1/cos 2y dy = ∫ dx
∫ sec 2y (1) dy = ∫ dx
∫ sec2y (sec 2y +tan 2y)/(s ...
Log 发表于 12-8-2010 08:47 PM

log大哥，这不是Maths T的differential equation吗？

wy07

y=e^x+4e^-2xfind the coordinate and nature of the stationary points.
(ans: (ln 2,3) minimum point)





y=x^2 ln x
find all the points of inflexion.
(ans: e^-2/3 , -3e^-3/2)

wy07

y=e^x+4e^-2xfind the coordinate and nature of the stationary points.
(ans: (ln 2,3) minimum point)





y=x^2 ln x
find all the points of inflexion.
(ans: e^-2/3 , -3e^-3/2)

wy07

y=e^x+4e^-2xfind the coordinate and nature of the stationary points.
(ans: (ln 2,3) minimum point)





y=x^2 ln x
find all the points of inflexion.
(ans: e^-2/3 , -3e^-3/2)

芭樂

Given that y=sin x/x^2  , x>0, prove that x^2  (d^2 y)/(dx^2 )+4x dy/dx+(x^2+2)y=0

谢谢

Allmaths

Given that y=sin x/x^2  , x>0, prove that x^2  (d^2 y)/(dx^2 )+4x dy/dx+(x^2+2)y=0

谢谢
芭樂 发表于 14-8-2010 07:59 PM

y=sin x/x^2
(x^2)y=sin x
(x^2)(dy/dx)+2xy=cos x
(x^2)(d^2y/dx^2)+2x(dy/dx)+2x(dy/dx)+2y=-sin x
(x^2)(d^2y/dx^2)+4x(dy/dx)+2y+sin x=0
(x^2)(d^2y/dx^2)+4x(dy/dx)+2y+(x^2)y=0
(x^2)(d^2y/dx^2)+4x(dy/dx)+(x^2+2)y=0

Log

回复 1525# Allmaths
发错了！发到这里

芭樂

Find the value of k if x/((x+1)^2 (x-k))  has a stationary point

Allmaths

Find the value of k if x/((x+1)^2 (x-k))  has a stationary point
芭樂 发表于 15-8-2010 10:54 AM

方便写下答案吗?

芭樂

A spherical balloon is inflated bt gas being such that its volume is increasing at a constant rate. Show that the rate of increase of the surface area of the balloon is incersely proportional to its radius.
谢谢

Allmaths

Find the value of k if x/((x+1)^2 (x-k))  has a stationary point
芭樂 发表于 15-8-2010 10:54 AM

blazex

Find the value of
n
∑r(r!)
r=1

Allmaths

Find the value of
n
∑r(r!)
r=1
blazex 发表于 15-8-2010 05:56 PM

之前log大哥已经解答了...

http://cforum1.cari.com.my/viewthread.php?tid=1513746&extra=page%3D1&page=54



1343 楼..

whyyie

peaceboy

A spherical balloon is inflated bt gas being such that its volume is increasing at a constant rate.  ...
芭樂 发表于 15-8-2010 11:41 AM

A =4 pi r^2
da/dr = 8 pi r  

就酱呱

Allmaths

whyyie 发表于 15-8-2010 06:41 PM

题目写错了...应该是 r/s..不是 (r/s)^(1/2)...