- #1
Felafel
- 171
- 0
hi everyone, I've found this exercise on a textbook and it doesn't resemble any exercise I've seen before. I just want to know how to proceed, you don't have to solve it for me :)
Study the continuity of the following functions, defined by:
1- f(x) = lim (n^x-n^-x)/(n^x+n^-x) x∈|R
n->+∞
2- f(x) = lim [ln(e^n+x^n)]/n x∈|R
n->+∞
A function is continuos if its limit L exists and it equals f(L).
But the limit here is to +∞!
So, after computing the two limits for the given n->+∞, how do I go on studying the finction?
Many thanksss
Homework Statement
Study the continuity of the following functions, defined by:
1- f(x) = lim (n^x-n^-x)/(n^x+n^-x) x∈|R
n->+∞
2- f(x) = lim [ln(e^n+x^n)]/n x∈|R
n->+∞
The Attempt at a Solution
A function is continuos if its limit L exists and it equals f(L).
But the limit here is to +∞!
So, after computing the two limits for the given n->+∞, how do I go on studying the finction?
Many thanksss