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Question: Limit approaching infinity of Arcsin

Question:Limit approaching infinity of Arcsin

tsw303 8
February 28 2008
0 
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.


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.
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