have you seen the definition of e ?
e = lim(1 + 1/n)^n as n --> ∞
or e = lim(1 + n)^(1/n) as n ---> 0
now look at your limit, does it not resemble my last statement?
lim(1+sinx)^(cscx) as x ---> 0
= lim(1+sinx)^(1/sinx) as x ---> 0
= e = 2.7182818...
you can test this on a calculator
set it to radians, and let x = .000001
I get 2.71828147, pretty close to e
limit as x-> 0
(1+sinx)^(cscx)
How do I show that this is indeterminate? Can I say that 1^(1/0) = 1^infinity?
3 answers
I don't need the limit, I just want to know how to show it is in the indeterminate form.
But..
as I showed in my solution, it isn't indeterminate,
it works out to the constant e, or 2.7....
as I showed in my solution, it isn't indeterminate,
it works out to the constant e, or 2.7....