,,,,,,,,

Last edited:

#### blamocur

##### Full Member
ég tala ekki þýsku

##### New member
ég tala ekki þýsku
You can ignore the first one, the rest is as mentioned in the title of the thread.

#### Dr.Peterson

##### Elite Member
I can't even tell how many separate questions there are here (there are two "part b"s!), or what the instructions apply to.

#### JeffM

##### Elite Member
I am fuzzy on what is going on after n [imath]\ge[/imath] 1, but I think this starts

It can be proved by complete induction that:

$f(x) = x \cdot sin(x) \implies \text {the n}^{th} \text { derivative} = x \cdot sin \left (x + \dfrac{n \pi}{2} \right ) + n \cdot sin \left ( x + \dfrac{(n - 1) \pi}{2} \right ).$
I am guessing that “complete induction” is what we call “weak mathematical induction.” I suspect this theorem is to be used (rather than proved) to find the indicated limits.