Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

What is #lim_(xrarroo) ( 1 + ( r/x ) ) ^ x#, where r is any real number?

1 Answer

Oct 27, 2015

#lim_(xrarroo)(1+r/x)^x = e^r#

Explanation:

#(1+r/x)^x = ((1+r/x)^(x/r))^r#

Let #u = rx#.so this becomes #((1+1/u)^u)^r#

Note that as #xrarroo#, we also have #u rarroo#

So,

#lim_(xrarroo(1+r/x)^x = lim_(urarroo)((1+1/u)^u)^r#

# = (lim_(urarroo)(1+1/u)^u)^r#

# = e^r#

Related questions

See all questions in Determining One Sided Limits

Impact of this question

1851 views around the world

You can reuse this answer
Creative Commons License