Would you help me find the limit?

Question

$Lim_(xrarroo)arcsin((1-x)/(1+x))$

$sinx=yquad=>quadarcsiny=x$

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Answer 1 · 2017-12-22T12:50:22

See below.

$lim_(x->oo)(arcsin((1-x)/(1+x)))$

$((1-x)/(1+x))$

Divide by $x$

$((1/x-x/x)/(1/x+x/x))= ((1/x-1)/(1/x+1))$

as $x->oo$ , $color(white)(88)((1/x-1)/(1/x+1))->((0-1)/(0+1))=-1$

$:.$

$arcsin(-1)=(-pi)/2$

$:.$

$lim_(x->oo)(arcsin((1-x)/(1+x)))=-pi/2$