Here's the question you clicked on:
Brooke_army
Evaluate the following limit: lim (1+7/x)^x/12 x→∞
I got the number 0.583
the correct answer is 1.79. I'm not sure where i went wrong
how did you get 0.583 ? mind showing your work/steps ?
is it \( \large \frac{(1+7/x)^x}{12}\) or \( \large (1+7/x)^{x/12} \)
y=lim (1+7/x)^x/12 ln(y)=lim x/12 ln(1+7/x) \[\frac{ \ln(1+\frac{ 7 }{x} }{\frac{12 }x }\]
mathmate it's the second
\[\lim_{x \rightarrow ∞} \frac{ (1+7)^x }{ 12 }\]
then i took d/dx to both the numerator and the denominator
the problem is \[\lim_{x \rightarrow \infty} (1+\frac{ 7 }{ 12})^\frac{ x }{12 }\]
In order to use L'hopitals rule, you must have a fraction with a function on the numerator and denominator
do you know a general formula \[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=...?\]
if you know ^ that, then you can put 7/x = y in your limit question first, to bring in that form.
if you use the formula, you get the correct answer in just few steps by adjusting the exponent. \[\lim_{y \rightarrow 0} (1+y)^{\frac{ 1}{y}}=e\]
im trying that right now
okay :) take your time...
thanks i got the right answer
good! you're welcome ^_^