anonymous
  • anonymous
Evaluate the following limit: lim (1+7/x)^x/12 x→∞
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I got the number 0.583
anonymous
  • anonymous
the correct answer is 1.79. I'm not sure where i went wrong
hartnn
  • hartnn
how did you get 0.583 ? mind showing your work/steps ?

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mathmate
  • mathmate
is it \( \large \frac{(1+7/x)^x}{12}\) or \( \large (1+7/x)^{x/12} \)
anonymous
  • anonymous
y=lim (1+7/x)^x/12 ln(y)=lim x/12 ln(1+7/x) \[\frac{ \ln(1+\frac{ 7 }{x} }{\frac{12 }x }\]
anonymous
  • anonymous
mathmate it's the second
abb0t
  • abb0t
\[\lim_{x \rightarrow ∞} \frac{ (1+7)^x }{ 12 }\]
anonymous
  • anonymous
then i took d/dx to both the numerator and the denominator
anonymous
  • anonymous
the problem is \[\lim_{x \rightarrow \infty} (1+\frac{ 7 }{ 12})^\frac{ x }{12 }\]
abb0t
  • abb0t
In order to use L'hopitals rule, you must have a fraction with a function on the numerator and denominator
hartnn
  • hartnn
do you know a general formula \[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=...?\]
hartnn
  • hartnn
if you know ^ that, then you can put 7/x = y in your limit question first, to bring in that form.
hartnn
  • hartnn
if you use the formula, you get the correct answer in just few steps by adjusting the exponent. \[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=e\]
anonymous
  • anonymous
im trying that right now
hartnn
  • hartnn
okay :) take your time...
anonymous
  • anonymous
thanks i got the right answer
hartnn
  • hartnn
good! you're welcome ^_^

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