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## 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.