LIMITS OF TRIGONOMETRIC FUNCTIONS by fad10689

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									         LIMITS OF TRIGONOMETRIC FUNCTIONS

limsin x = 0 .
x →0
limcos x = 1 .
x →0
lim tan x = 0 .
x →0


VERY IMPORTANT LIMIT
     sin x
lim        =1
x →0   x

NOTE: YOU CAN’T SAY THAT
     sin x 0
lim       = = 1 BECAUSE THE LIMIT LAW NUMBER 3
x →0   x   0
REQUIRES lim g ( x ) ≠ 0 , AND IN THIS ONE, lim x = 0
                x →a                       x →0


PROOF (GEOMETRIC ARGUMENT):
(WE’LL USE θ INSTEAD OF x , BECAUSE WE’RE USING
THE DIAGRAM BELOW.)
                       π
ASSUME 0 < θ <           .
                       2
IN THE DIAGRAM AT THE RIGHT,
NOTE THAT
 PQ = sinθ ,
PS = tanθ , AND
PR = θ
THEN, FROM THE DIAGRAM,

WE SEE THAT sinθ < θ < tanθ ,

								
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