IIT JEE , AIEEE Forum - Mathematics , Differential Calculus - how do i draw d graphs of greatest integer functions n fractional part of functions???

paulo

plzzzz help

paulo

sum1 plzzzz............

nivedh_89

The greatest integer function, y = [x] is defined as follows: [x] is the greatest integer that is less than or equal to x.

spideyunlimited

hang on ill post the graphs

spideyunlimited

here are the graphs of the two functions..
nudge me if you have doubts.

*PLZ RATE*

paulo

how do i draw specific graphs like [sinx] and {sinx}.....im stuck coz of these conceptual doubts

paulo

hey...thnx a lot....yea n ill rate u

spideyunlimited

if u have f(x) and u have to draw graph of mod f(x)
let y = | f(x) |
draw the graph of f(x) ( ex. cos or sin)
then as y will always be positive... ( because it is mod. of something) reflect all parts of graph which are in negative region of y axis onto the positive axis of y ..

spideyunlimited

rate me plz lol :) .. nd tell me if u still havent understood how to make the mod graphs

paulo

i noe d mod graphs ......wod i actually wanted to know was {sinx}fractional part,

[sinx] []=greatest intregral fn.

.

spideyunlimited

sinx varies between -1 to 1
so
while sin x is [-1,0) .. [] will be -1 ....{} will be from 0 to 1
sin x is [0,1) ....[] will be 0 ...{} will be from 0 to 1
when sin x is 1 ...[] will be 1...{} will be from 0 to 1

1 is not included in {}

spideyunlimited

draw the graph of sinx and see where its value is what.. and for tht value put the required function

neeraj_agarwal_1990

To draw [sinx]...
1) draw graph of sinx
2) draw y =k lines....where k is an integer...
i.e. draw y=-2,y=-1,y=0,y=1....etc..

2) find points where the meet the graph of sinx.these are critical points...

3) keeping the critical points at there original place ...shift the graph b/w the two consecutive y=k lines to the lower line....

this will give u the required graph...

neeraj_agarwal_1990

For {sinx}...
1) draw sinx

2) draw y =k lines....where k is an integer...
i.e. draw y=-2,y=-1,y=0,y=1....etc..

3) shift the graph b.w two consecutive lines to the interval y (- [0,1).

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