Question

is xcosx periodic

Answer 1

here is a site that will allow you to graph it

https://www.desmos.com/calculator

Answer 2

No it is not..its an increasing function

Answer 3

why give an answer.... let the user investigate it...

Answer 4

giving an answer motivates the asker

Answer 5

to do what....?

Answer 6

to post more questions

Answer 7

no it's not

Answer 8

lol... yep... and lots of understanding in that.... someone else answering homework with out any learning.... that's sad

Answer 9

ok i got it its not periodic but how to argue about it without using a graph?

Answer 10

it doesn't repeat itself after certain intervals

Answer 11

but to see if it repeats itself or not we have to graph it...how can we tell without using a graph ?is there any other logical reason?

Answer 12

well if the standard form of the cos function is

y=acos(x)

then the amplitude is a...

but with

y = x cos(x)

as x increases

y = x cos(x) increase....

so perhaps you could should its divergent

Answer 13

but that's just a guess...

Answer 14

ok now can you tell why sin(1/x) is not periodic without using graph?

Answer 15

there is a discontinuity in the domain of x, so the curve isn't continuous

hence its not periodic

1/x x cannot = 0

does that make sense

Answer 16

I don't think that's the reason tan x is also discontinuous at pie/2

Answer 17

what I can think of is 1/x will be very to close to zero sin x is approximately equal to x for values closer to zero , that's why its not periodic

Answer 18

well a simple definition of a period function is that it replicates itself... repeatedly...

so it there is a discontinuity... then it can't replicate itself...

Answer 19

isn't the graph of tan x discontinuous at pie/2 , so it shouldn't be periodic by the same logic

Answer 20

and to prove its periodic you can use

shown that there is some number p so that

f(x+ p) = f(x)

and in terms of tan

tan = sin/cos so cos cannot be zero...

so again a discontinuity occurs...

periodic functions are continuous...

Answer 21

what do u mean to say...that tanx is not a periodic function.

Answer 22

well it has asymptotes at -pi/2, pi/2, 3pi/2....

the curve as gaps in it...

Answer 23

tan(x) is not continuous... and that's the key to periodic graphs

Answer 24

tanx is not continuous but its periodic right?

Answer 25

just to add to the first question :
clearly xcosx is not periodic as the amplitude is not fixed
but its frequency is fixed, so its somewhat periodic in the sense that it cuts the x-axis periodically

Answer 26

thanks all

Answer 27

any luck on proving sin(1/x) not periodic ?

Answer 28

maybe u can try proof by contradiction :

say, sin(1/x) is periodic and the period is \(T\),
then below holds : \[\sin(1/x) = \sin (1/x + T)\]

Answer 29

can u elaborate you ans.

Answer 30

I haven't worked anything yet lol, leme think a bit more :)

Answer 31

its ok take ur time ! btw thanks for ur help ;)

Answer 32

Look up second reply here :
http://math.stackexchange.com/questions/282644/is-fx-sinx2-periodic