21graf by ani is very much crrct, this is jus a specification wich I feel wud b satisfied......
21 Answers
62Hint: Draw the originial curve without taking greatest integer.. and then think!!
2121no i was jus saying dat..... the graf is a non- repeater.......
ie ek bar y = t(say) aa gaya for particular value of [x] ........
then ther will b no other [x] such that its y = t;
IS THIS RITE OR NOT??
62tapan can you draw the graph!..
ani has already done that..
i was giving a hint to srinath!
21y = √2*sin([x] - Π/4)
[x] is periodic with 1, sin is periodic wid 2Î ;
this means : only wen [x] changes by a magnitude 2Î *n can v hav da same value of y for two diff values of [x].....
as [k] - [t] = integer ≠2Π*n ..................... (n = natural no.)
ther will b no same value of y for 2 diff [x].... I repeat [x] not x kyunki vo to hone hi vala hai!!
Sir, wat else do u want us 2 find in this un, if ne!!!!
62somewhat ok
hInt: the graph will have one tail fixed to the graph of
sin x - cos x
does this hint help?
1it lies in b/w two graphs like this no?thoda wrong hai lekin idea is ok no?
62i mean why this is the graph that u got.. and how do u extend it on both sides of the real line?
62lol.. nothing to be sad and all... if u can still find why this is happening?
11B/w 0 and 1 y is sin0-cos0 which is -1
b/w 1 and 2, y is sin57°-cos57° which is some value less than 1 (assuming 1 rad ≈ 57°)
B/w 2 and 3, y is sin114°-cos114° which is some value >1 as sin114>0 and cos114<0
B/w 3 and 4, y is sin171°-cos171° which is again some value >1 for the same reason
B/w 4 and 5, y is sin228°-cos228° which is a small negative value (as I shamelessly calculated [2])
B/w 5 ans 6, y is sin285°-cos285°, which again i shamelessly calculated [2]
I AM SO SORRY GUYS. I WRECKED THE OPPORTUNITY OF THOSE WHO WOULD HAVE POSTED THE CORRECT GRAPH WITHOUT USING A CALCULATOR.
[2][2][2][2][2]
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62that you will have to do.. ...
but this is correct....
how do u explain it a bit better? cos this makes no sense... to normal eyes.... !!
62domain is real line..
you dont need to do it for the whole real line... just a interval will do.. :)