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#