DLS
Limits question [Challenge]
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DLS
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\[\LARGE \lim_{x \rightarrow 0} \frac{(1+x)^\frac{1}{x} -e}{x}\]
DLS
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@yrelhan4 @shubhamsrg
shubhamsrg
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*
:)
DLS
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first time in life :O
ParthKohli
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Taylor Series expansion?
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Use whatever you want.
ParthKohli
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Ans 0?
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Nope
experimentX
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Taylor series works
ParthKohli
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Weird. The Taylor Series expansion is in the terms of \(e\) and \(x\). The first term is \(e\)
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Taylor series gives 0?
experimentX
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gives -e/2 if you calculate correctly
ParthKohli
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Oh wait! lol, yeah. I forgot to consider that -e/2 which had no \(x\)
DLS
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How about a different way rather than taylor series?
ParthKohli
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Definition of derivative? :-|
DLS
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o.O
ParthKohli
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I was just thinking how this might be the definition of a derivative in disguise.
experimentX
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Binomial expansion might work ... but that's too long
ParthKohli
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DLS
Use whatever you want.
15 minutes ago
DLS
How about a different way rather than taylor series?
9 minutes ago
DLS
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You are right,still investigating for more methods,I wrote so to specify that you are not bound to any particular method,just asking if you know anything alternate :)
experimentX
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L'hopital works