Question

Any1 Help!?
Ok so i was working on question

Answer 1

In which following function was given \[f(x) = a_{n} + \sin(\pi)X for x \in [2n ,2n+1]\]

Answer 2

and f(x) = \[b _{n} + \cos (\pi) x for x \in (2n-1,2n)\]

Answer 3

now while going through the solution in the book , i came across this \[f(2n+1)^{+}) = b _{n+1}-1 \]

Answer 4

i dint get it , How is RHL of f(x) approaches 2n+1 is \[b _{n+1}-1\]

Answer 5

i dint get the \[b _{n+1}\] Part , How come we get this?

Answer 6

@Loser66

Answer 7

This is the ^ link to the whole question

Answer 8

@jdoe0001

Answer 9

@radar

Answer 10

@skullpatrol

Answer 11

If you're wondering where that +1 comes from, it's because Cos(2kpi) where k is an integer is always 1.

Answer 12

actually i got that i m wondering abt bn+1 part

Answer 13

Oh you mean \[b_{n+1}\]

Answer 14

Yes!

Answer 15

Ah I see.. They're checking the last endpoint, x = 2n+1

Answer 16

the first part is fine:\[a_n+Sin\pi x\]is defined on [2n, 2n+1]

Answer 17

yes, I m confused abt the second part :(

Answer 18

\[b_n+Cos\pi x\]is only defined on (2n-1, 2n), I think they're just incrementing everything for that reason

Answer 19

I mean the ns

Answer 20

hmm, yea but why increment n by 1. as it is defiend on (2n-1,2n) so if we have to increment by 1 that wud be for 2n , for 2n+1 we should be incrementing by 2? idk i m confused

Answer 21

something like:\[b_{n+1}+Cos\pi x\]being defined on: (2n-1+1, 2n+1)

Answer 22

hmmm

Answer 23

sounds legit

Answer 24

or at least that's what i think they're doing. they don't need to add 2, as that's not required by the question

Answer 25

but RHL of 2n+1 wud be value greater than 2n+1 , it doesnt contain in (2n-1+1,2n+1) interval, what do u think?

Answer 26

for LHL we can use (2n-1+1,2n+1) , but for RHL that interval would not be valid, dont u think so?

Answer 27

true...

Answer 28

@phi can you explain this to us?
http://assets.openstudy.com/updates/attachments/52f7f86be4b043c0f358e674-cybershadow-1391985919363-img.png

Answer 29

i think u have a mod helping you- your fine :P

Answer 30

First, these functions abut each other as we increase n, alternating a+ sin, b+cos,