arctgx/x=1高手请帮忙证一下（从arcsinx/x=1推）注：是求极限啊，证limarctgx/x=1,由limsinx/x=1来推,x趋向0时

Question

arctgx/x=1
高手请帮忙证一下（从arcsinx/x=1推）
注：是求极限啊，证lim arctgx/x=1,由lim sinx/x=1来推,x趋向0时

Answer 1

令
y=arctg(x)
x=tg(y)
tg(y)=sin(y)/cos(y)
x->0 y->0,tgy ->0
lim arctgx/x
=lim y/tg(y)
=lim (y*cos(y))/sin(y)
=(lim cos(y))*lim (y/siny)
=1*1
=1