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limx→0 (sin5x)/2x

and

limx→0 (tanx)/(xsecx)

 

i wanted to check if my answers and work were all right ! (5/2 and 1) thank youuuu:))))))

 Nov 19, 2018
 #1
avatar+107348 
+1

sin (5x) / 2x    multiply top/bottom by 5

 

5sin (5x) / [ 5 * 2x]

 

(5/ 2)  sin (5x) / [ 5x]

 

As x  ⇒  0  the limit   of  sin (5x) / [5x}  = limit of  sin (0) / 0   =  1

 

So....5/2    is correct !!!!

 

 

tan x              sinx / cosx                      sin x * cos x            sin x

_____    =      ____________ =          ___________ =      _____

xsecx               x  [ 1 /  cos x]               x * cos x                   x

 

 

And the limit  of the last function as x ⇒ 0   =   1     !!!!

 

Correct on both counts !!!

 

 

 

cool cool cool

 Nov 19, 2018

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