Graph of the Day - 21-04-09

9

Celestine preetham ·2009-04-21 07:22:11

ok its a kind of implicit

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62

Lokesh Verma ·2009-04-22 01:18:54

yes perfect celestine..

so it gives a contradiction to our assumption that

[x]=n

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9

Celestine preetham ·2009-04-22 01:14:09

if sin n is negative [n+sin n]=n-1

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11

Mani Pal Singh ·2009-04-22 00:52:53

it is because of the fact that {-x}=1-{x}

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62

Lokesh Verma ·2009-04-22 00:51:51

see the answre is

n+sin n (for all integers n such that sin n is positive. )

If sin n is -ve there will be no solution... :)

Can you reason out why the above is true.

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9

Celestine preetham ·2009-04-22 00:35:05

hmm post 13 still pinked ?

nishant sir see #17

also even when positive can u guarentee [n + sin n] =n ???

what if sin n is negative

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1

palani ............... ·2009-04-21 12:51:08

found some solns
sin n +n

0,
1.84,
2.909,
3.14,
etc........

if x lies b/w(2n\pi ,(2n+1)\pi )
den
der would be 3 soln for every value of n
in d other region sin x<0 no soln

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11

Mani Pal Singh ·2009-04-21 12:07:13

thats y the disscussion is goin on
TO FIND A SEQUENCE
nishant sir thinks (have ) a sequence
but we don't think so

check whether u may prove to be useful

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1

palani ............... ·2009-04-21 12:04:26

i dont think so d soln. is in any sequence

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11

Mani Pal Singh ·2009-04-21 11:58:53

but how will u find a solution[12][12][12]

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1

palani ............... ·2009-04-21 11:43:38

just consider LHS &RHS seperate function &superimpose dem

werever both d functions intersect they bcomz d soln

y=\begin{Bmatrix} x \end{Bmatrix}

z=sin[x]

den plot dem

[/img][/img]

a little more in nxt post

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9

Celestine preetham ·2009-04-21 09:41:59

this q isnt solvable dont worry !!!!

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11

Mani Pal Singh ·2009-04-21 08:22:19

yup its not thateasy
its a gr8 headache 4 me !!!!!!!!1

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9

Celestine preetham ·2009-04-21 08:20:39

its not n+ sinn chk for -1

also theres a lot of other things nishant bhaiyya has overlooked

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1

Philip Calvert ·2009-04-21 07:32:46

! he's gone offline [2]
celestine what do u say

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1

Philip Calvert ·2009-04-21 07:27:45

bhaiyya
what about n = 6 in
n+sin n

LHS is positive RHS is negative !

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11

Anirudh Narayanan ·2009-04-21 05:00:32

hmmm a bit confusing

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9

Celestine preetham ·2009-04-21 07:16:42

i dont agree see when n is negative

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62

Lokesh Verma ·2009-04-21 06:49:21

yes celestine

the graph will be lines parallel to the y axis passing thru the points

n+ sin n

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9

Celestine preetham ·2009-04-21 06:46:18

byah is there a graph ?? see abv post

also i know the solutions

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1

Philip Calvert ·2009-04-21 06:38:06

yes
n +sin n
exactly

especially bcos sin(n) will never belong to N

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62

Lokesh Verma ·2009-04-21 06:36:16

yes celestine

In the hind sight it should not have been on the graph of the day...

And yeah philip the answer is quite straight forward

x = n+ sin (n) for all integers n :)

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1

Philip Calvert ·2009-04-21 06:33:12

i think its quite straightforward !

sin 2 = 0.034899496702500971645995181625333

so x = 2.034899496702500971645995181625333

similarly
for all further values
i dont know how to do without a calc

ofcourse we have to neglect places where sin goes -ive

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11

Anirudh Narayanan ·2009-04-21 06:33:05

celestine, the graph will be of the form x=k.....lines parallel to the y-axis

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9

Celestine preetham ·2009-04-21 06:29:16

why is this posted in Graph of the day ???

we cant draw graphs out of abv question as y is not invlolved

btw do u want us to find the solutions of x ??

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62

Lokesh Verma ·2009-04-21 06:26:45

loll

you guys have been stumped on this simplest(?) graph

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11

Anirudh Narayanan ·2009-04-21 06:22:00

any value of [x] will be an integer.....so?

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62

Lokesh Verma ·2009-04-21 06:20:21

Hint: take any value of [x]

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11

Mani Pal Singh ·2009-04-21 06:11:27

Notice that RHS and LHS are independent of each other! (Or are they?)

[7][7][7]

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62

Lokesh Verma ·2009-04-21 05:20:44

anirudh you have done most of the hardwork already!!

Notice that RHS and LHS are independent of each other! (Or are they?)

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