# Lim x->0+ (x^cos(1/x))

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1. May 6, 2017

### Snen

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
let y = lim x->0+ x^cos(1/x)
lny = cos(1/x)*lnx = (x*cos(1/x)) * (lnx/x)

x*cos(1/x) = 0 (sandwich theorem)
lnx/x = 0 (l'hopital)
so lny = 0
and y = 1
Is this correct?

2. May 6, 2017

### PeroK

No, that doesn't look right at all.

what happens when $\cos(1/x)$ is negative?

3. May 6, 2017

### Snen

Well then y would tend to infinity but the limit is x-> 0+

4. May 6, 2017