Hi there,
I'm currently stuck on a maths question.
Find the limit as x approaches 0 for (1+sinx)^cotx
I've put logs on both sides and am attempting to use hopitals rule but don't know where to proceed from here.
let's use an intuitive approach
You might recall that
lim (1 + 1/n)^n = e as n ---> ∞
or
lim (1 + n)^(1/n) = e , as n ---> 0
now we have (1+sinx)^(1/tanx)
now as x ---> 0 , sinx --->0 and 1/tanx ----> ∞
so we have
(1 + really small)^really large
which is e
test: on my calculator, I let x = .000001
and got
(1+sin(.000001)^(1/tan.000001)
= (1+.000001)^1000000
= 2.718280469
and e = 2.718281828 , not bad eh?