...not as long as Mathstud's. So feel free to create a new one
Some (if not all) are easy, so @ the masters (not http://www.mathhelpforum.com/math-he...s/masters.html), pardon me for insulting your abilities and please lend normal people 10 more minutes than you need for solving them
Of course,
(you may be able to use the gradient definition). No power series is needed but approximations could be needed in some limits.
I think solutions can all be less than 5 or 6 lines...
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Solution #1 (Chris L T521) & book's answer
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Solution #1 (Mathstud)
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Solution #1 (Mathstud)
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Solution #1 (Mathstud)
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Solution #1 (Mathstud)
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Solution #1 (Mathstud)
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Have fun
No Root & Ratio test trick either ^^ If you want to, it's ok, but I don't really like this method (never saw it in books )
No integral is needed either but yes you can do it this way.
There are various ways of solving the limits. But as far as I can see, no use of big tricks like integrals or power series.
(hey, don't quote the whole post !!!! it's painful for internet connections )
I guess I am an an inovator
No integral is needed either but yes you can do it this way.
There are various ways of solving the limits.
(hey, don't quote the whole post !!!! it's painful for internet connections )
Then you must have some kind of method you prefer! I would love more restrictions since I can do these mostly with one or two methods. But if you say you can only use _____ method it will be harder! Your call though. This is entirely your thread.
And I deleted some of the quote
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By the way, is that the correct answer?
Looks weird though
There's no particular method I advocate, I read it in a book and I liked them all.Then you must have some kind of method you prefer! I would love more restrictions since I can do these mostly with one or two methods. But if you say you can only use _____ method it will be harder! Your call though. This is entirely your thread.
But I think using integrals and power series sometimes just kills too fast the problem
Use substitutions, approximations, gradient definition and TRICKS and your INTUITION
ThanksAnd I deleted some of the quote
I forgot to tell ya, yes it is ^^By the way, is that the correct answer?
I'll put a red sign rather when it is false than when it is correct
Let
So as
So we have
Now let us consider these two limits seperately
Firstly
Now let
So we have that s
Giving us
Now I do not know if this suffices but
So
Now consider
So
Once again let
Giving us
Now if you don't allow precs then
This implies that
This now implies that
This implies by the squeeze Theorem that
So now seeing that
So