Thursday, 9 January 2020

real analysis - How to find limhrightarrow0fracsin(ha)h



How to find limh0sin(ha)h without lhopital rule?

I know when I use lhopital I easy get

limh0cos(ah)a1=a

but I don't know how to behave without that way


Answer



Hint:



sin(ha)h=asin(ha)ha



Also, remember what limx0sin(x)x

is equal to?


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real analysis - How to find limhrightarrow0fracsin(ha)h

How to find limh0sin(ha)h without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...