请问几个数学题~~

外星護法

1） (a) Show that sin^2 x + (1/2) cos x =  17/16 - (cos x - (1/4))^2

Hence or otherwise, state the range of 1/(2sin^2 x + cos x - 1)  for 0 < x < 2pi...

show 的我找到了，可是怎样state the range ???



2)        -1 < cos x < 1

         -5/4  < cos x - 1/4 <  3/4

           ?  < (cos x - 1/4)^2  < ?        请问我的range会变成多少 ？？？


3.)When 1000^2008 is written as a numeral, the number of digits written is ??
请问题目在问什么 ？？ 什么是 numeral ? 要怎样做这类的题目 ？？

4.） 什么是 toggle function ??  A function is said to be a toggle function on (p,q,r) if f(p) = q, f(q)=r and f(r)=p.
       The function f(x) = ax*2 + bx + c is a toggle function on (1,2.3). What is the value of c ?

5.) How many numbers from 1,2,3,4,.....2008 have a cubic number other than 1 as a factor ???

谢谢~~~

HanQing

Well, willing to help though my maths not very good at this level.
For question 1

same method could be applied to question 2

For question 4,


hope it helps

~Lucifer~

第2题，应该跟着square就行了。
第3题，应该是问1000^2008写成号码，会有多少个digits。
如，10^4=10000,有5个digits。