Better Students Ask More Questions.
Question about Calculus (Limit)...?In my Textbook, the question is: Show that : lim...
1 Answer | add yours
`Put 1 + 1/x = t =gt 1/x = t - 1 =gt x = 1/(t-1)`
Calculate logarithms both sides:
`ln x = ln(1/(t-1))`
`` Use quotient property of logarithms:
ln x = ln1 - ln (t-1)
ln 1 = 0 =>
`ln x = - ln (t-1)`
Write the function using variable t:
t^(1/(t-1)) => `lim_(t-gtoo)` `t^(1/(t-1))` = `lim_(t->oo)` `(1 + t - 1)^(1/(t-1)) ` (you must add and subtract 1 in the brackets and create the form `(1+a_n)^(1/a_n)).` Calculate the limit:
`lim_(t->oo)` [1 + (t-1)]^1/(t-1) = e
Posted by sciencesolve on December 1, 2011 at 11:11 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.