Since sin(h)-> as h-> 0 this is of the form "0/0" anmd L'Hospital rule can be used.
Differentiating num and den yields
cos[sin(h)]*cos(h)/cos(h)->1/1=1 as h->0.
Differentiating num and den yields
cos[sin(h)]*cos(h)/cos(h)->1/1=1 as h->0.
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Let sin h = x
ReplyDeleteWhen h tends to 0, x tends to 0
Therefore,
lim x tends to 0 sin x/x = 1