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Yahoo!
 3 years ago
\[\lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^x }{ n })^{\frac{ 1 }{ x }}\]
Yahoo!
 3 years ago
\[\lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^x }{ n })^{\frac{ 1 }{ x }}\]

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Yahoo!
 3 years ago
Best ResponseYou've already chosen the best response.0Power is For Both nume and Deno

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2can be solved by taking log on both sides...

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2and also without LH, do you know what lim x>0 [a^x1 /x] =... ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2\[\lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^x }{ n })^{\frac{ 1 }{ x }}\\=\lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^x +nn}{ n })^{\frac{ 1 }{ x }} \\ \lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^x+n }{ n }1)^{\frac{ 1 }{ x }} \\\lim_{x \rightarrow 0}(\frac{ 1^x1 + 2^x 1+ 3 ^x1 ........n^x1 }{ n }1)^{\frac{ 1 }{ x }}\] got the hint ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2and you need to take log on both sides first....to get 'x' in the denominator.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2am i on right track? @experimentX

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2seems so ... ;let me do on copy!!

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2oh .. that last one is +1

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2\[\lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^x }{ n })^{\frac{ 1 }{ x }}\\=\lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^x +nn}{ n })^{\frac{ 1 }{ x }} \\ \lim_{x \rightarrow 0}(\frac{ 1^x + 2^x + 3 ^x ........n^xn }{ n }+1)^{\frac{ 1 }{ x }} \\\lim_{x \rightarrow 0}(\frac{ 1^x1 + 2^x 1+ 3 ^x1 ........n^x1 }{ n }+1)^{\frac{ 1 }{ x }}\]

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2although ... L'hopital seems a bit faster!!

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2LH after taking log, right ?

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2yeah!! your method works just fine as well!!

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2hmm...much faster! thanks~

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2oh!! i had been using unnecessary approximations. your method is faster!!

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2should be n! e^(1/n)

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2woops!! sorry (n!)^(1/n)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2using the standard formula for lim x>0 (1+x)^(1/x) and adjusting the exponents .

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2the other would be use the usual unusual trick!! x = e^ln(x)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2haven't practised that much...would like to see steps, if you don't mind...

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2why do i feel i have asked this limit Q..... O.o, @Yahoo! where are you ?

Yahoo!
 3 years ago
Best ResponseYou've already chosen the best response.0i also..Need to know the steps Plzz

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1357499465779:dw

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1357499559730:dw

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1357499607470:dw

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2that's same as @hartnn 's dw:1357499736048:dw

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2x = e^ln(x) is the usual trick for types of f(x)^g(x) like ... n>0 (n!)^(1/n^n)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2got your steps :) thank you!

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0i can't think of another way at all you are going to have to either take the log or rewrite as an exponential (which is really the same thing) because you have a variable in the exponent

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.2dw:1357578176065:dw
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