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+1
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avatar+275 

Find the limit.

 

lim         sin(6x) / x + tan(9x)

x→0

 Mar 1, 2019
 #1
avatar+27547 
+1

When theta is very small then sin(theta) → theta, and tan(theta)→theta

 

So sin(6x)/x + tan(9x) → 6x/x + 9x = 6 + 0 = 6 as x tends to zero

 Mar 1, 2019
edited by Alan  Mar 1, 2019
 #2
avatar+98130 
+2

I think this also might be

 

 

lim         sin(6x) / [ x + tan(9x) ]

x→0

 

Using L'Hopital's Rule we have

 

 

lim         6cos(6x) /[ 1 + 9sec^2(9x) ]    =     6(1)  / [ 1 + 9 ]  =  6 /10    =  3 / 5

x→0

 

 

cool cool cool

 Mar 1, 2019

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