...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)

Alternative

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Solution #1 (Mathstud)

Alternative

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Solution #1 (Mathstud)

Alternative

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Solution #1 (Mathstud)

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Solution #1 (Mathstud)

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Have fun