mmmladenov1
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Please help to find the limit with hopital's rule
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mmmladenov1
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You can ignore the first one, the rest is as mentioned in the title of the thread.ég tala ekki þýsku
Dr.Peterson
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I can't even tell how many separate questions there are here (there are two "part b"s!), or what the instructions apply to.
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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:
[math]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 ).[/math]
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.
It can be proved by complete induction that:
[math]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 ).[/math]
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.