- #1
tsw303
- 7
- 0
Homework Statement
limit approaching infinity: (arcsin(x))/(x)
= 0
Question is: Why? The 'Sandwich Theorem' 0=[(arcsinx)/x]=0 gives this
solution, but looking at the graph of (arcsinx)/x , this appears
impossible.
Homework Equations
lim x->OO [arcsin(x)] - {DNE)
lim x->OO [(arcsinx)/x] - {DNE/OO}
lim x->OO [-Pi/2x] = lim x->OO [(arcsinx)/x] = lim x->OO [Pi/2x]
=> 0 = [(arcsinx)/x] = 0
=> lim x->OO [(arcsinx)/x] = 0
HOWEVER: (-Pi/2)<[arcsinx]<(Pi/2) ... SO ...
... (x) never reaches (OO) for (Pi/2x) to reach the limit x->OO (Pi/OO)
= 0.
The Attempt at a Solution
The sandwich theorem gives and answer of "0". Maple 11 gives the same answer, so does my teacher. This just doesn't seem possible.