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## #1 2007-03-13 18:45:51

Dharshi
Member
Registered: 2006-10-31
Posts: 56

### Anyone knows this??

Which of the following functions is non periodic ?
(a) f(x) = {x}, the fractional part of the number x
(b) f(x) = cot(x + 7)
(c) f(x) = 1  sin^2x/(1 + cotx)  cos^2x/(1 + tanx)
(d) f(x) = x + sinx

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## #2 2007-03-13 19:38:04

Stanley_Marsh
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Registered: 2006-12-13
Posts: 345

### Re: Anyone knows this??

Here a method , assume k are their period. Check out whether the equation F(x)=F(x+k) has a constant solution for k for any x.

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## #3 2007-03-13 20:07:17

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

### Re: Anyone knows this??

The first one, Let f(x)={x}={x+k} k must equally to any integers, the min period is 1
The second , let f(x)=cot(x+7)=cot(x+7+k) , since the period of cot is

then k=

Last edited by Stanley_Marsh (2007-03-13 20:08:25)

Numbers are the essence of the Universe

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## #4 2007-03-13 20:19:46

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

### Re: Anyone knows this??

The third one ,

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## #5 2007-03-13 20:25:38

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

### Re: Anyone knows this??

The fourth one ,

which is not below 0 , so the value of the function will always increase ,such function contains no period.

Numbers are the essence of the Universe

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## #6 2007-03-16 07:48:21

Prakash Panneer
Member
Registered: 2006-06-01
Posts: 110

### Re: Anyone knows this??

a) It is a fractional part. So, it is a periodic function.

b) Trigonometric function: It is also a periodic function.

c) Constant + or - Trig. function: Periodic function

d) Varibles +Trig : Non- periodic.

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## #7 2007-03-19 01:06:41

gig
Member
Registered: 2007-03-19
Posts: 3

### Re: Anyone knows this??

a piece of timber is cut in two lenghts in the ratio of 7:2. if the original piece of timber was 828 cm long,how long is the larger piece of the cut lenghts.

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## #8 2007-03-19 01:15:04

Maelwys
Member
Registered: 2007-02-02
Posts: 161

### Re: Anyone knows this??

gig wrote:

a piece of timber is cut in two lenghts in the ratio of 7:2. if the original piece of timber was 828 cm long,how long is the larger piece of the cut lenghts.

To figure this out, you have to do a couple steps.
- First, since the ratio is 7:2, you add those together to determine how many total "units" the timber can be broken into.
- Then divide the length by the number of units, to find the length of each unit.
- Then, simply multiplying the length of each unit by the number of units length you want to calculate will tell you how long that piece is.

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## #9 2007-03-19 05:36:21

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

### Re: Anyone knows this??

well , if a timber cut in 7:2 . you can think like this , 7 blocks of wood belong to A , 2 blocks of wood belong to B , then what is the total blocks of wood , the wood is cut in 7+2=9 blocks , then how long is each block , 828/9.   Then how long is 7 blocks together (larger) , (828/9)*7.

Numbers are the essence of the Universe

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