Question

let f(x)= ln(3+sin x)
is f periodic? if so what is its period? please explain.

Answer 1

thank you for helping me

Answer 2

No problem

Answer 3

as you can see this question looks like Chinese.

Answer 4

It makes sense, but the ln makes the situation complicated. The bit within the () is periodic, I have to double check on the ln

Answer 5

First of all, you understand what it wants by period, right?

Answer 6

yes. and I thought you need the formula 2pi/b but I don't see can b in this.

Answer 7

In this situation, I'm positive that the b=1, because there isn't any sort of coefficient directly in front of the x in sinx

Answer 8

First, we need to determine whether the ln removes it from a periodic equation.

Answer 9

https://www.desmos.com/calculator

Answer 10

looks periodic to me

Answer 11

That it does, so the period in this case appears to be 0-6.25

Answer 12

what?

Answer 13

how did u come to that conclusion

Answer 14

One moment, let me get the image

Answer 15

Do you understand?

Answer 16

0-6.25 is the period based on what info in that chart

Answer 17

Just the change in y from 0 to 6.25. Just eyeballing it, from my starting point at x=0, at x=6.25, the line of the graph appears to have returned to the same y position after having performed one loop of the equation. Does that make sense?

Answer 18

yes. thanks so much.

Answer 19

\(\sin x\) is \(2\pi\)-periodic, and so is \(3+\sin x\).

\(\ln x\) is defined for positive values of \(x\), which is true for \(3+\sin x\), since \(2\le3+\sin x\le4\). This means the function retains its periodicity.