How to prove that lim (x→0) sinx/x=1
without geometric method , without hospital

Question

How to prove that lim (x→0) sinx/x=1 
without geometric method , without hospital

kainui · Answer

Plug in values slightly larger or smaller than 0 and see what it approaches. So, try .1, .01,.001,.00000001, etc... and then make sure it matches on the other side.

amoodarya · Answer

ok I know it but 
I looking for an idea to give prove 
for example by sequences or something else 
but not use the derivative

kainui · Answer

Like an analysis proof? I'm not sure I know what level of rigor you're looking for. I feel like the geometric picture is proof enough, even more so than anything else. Just graphing sinx/x is good.

anonymous · Answer

I believe you use maclaurin series to prove it

amoodarya · Answer

Kainui 
I am  student of applied math in phd degree now 
I know all of <k12 or college method for the proof

amoodarya · Answer

sourwing 
thank for hint but the series based from derivation

primeralph · Answer

@amoodarya  Still need a formal proof?

primeralph · Answer

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