oblicz granice funkcji: sin7x/5x
sin ( 7x)/ ( 7x) = [ sin (7x)/ ( 7x)] *[ ( 7x)/(5x)] = ( 7/5) * [ sin (7x)/ ( 7x)]
czyli
lim [ sin ( 7x)/ 7 x] =
x -> 0
= lim ( 7/5)* [ sin ( 7x)/(7x) ] = 7/5
bo
lim sin ( 7x) / ( 7x ) = 1
===========================
Jest też taki wzór :
lim ( sin ( m x)]/ ( n x) = m/n
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sin ( 7x)/ ( 7x) = [ sin (7x)/ ( 7x)] *[ ( 7x)/(5x)] = ( 7/5) * [ sin (7x)/ ( 7x)]
czyli
lim [ sin ( 7x)/ 7 x] =
x -> 0
= lim ( 7/5)* [ sin ( 7x)/(7x) ] = 7/5
x -> 0
bo
lim sin ( 7x) / ( 7x ) = 1
x -> 0
===========================
Jest też taki wzór :
lim ( sin ( m x)]/ ( n x) = m/n
x -> 0
===========================