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avatar+322 

Find the limit.

lim x→0     sin(x9) / x

 Mar 2, 2019
 #1
avatar+18754 
+3

L'Hopitals Rule

 

Lim x ----.>0  (cos(9x) *9)/1  = lim x----> 0  9 cos(0) = 9

 Mar 2, 2019
 #2
avatar+102417 
+1

Thanks EP....here's another way not using L'Hopital's

 

 

lim                   sin (9x)

x → 0             ______              multiply top/bottom by 9

                          x

 

 

lim x → 0            9 sin (9x)

                       _________                let 9x =     θ

                              9x

 

 

lim x → 0          9 sin ( θ)

                        ________

                               θ

 

 

9   *       lim x → 0       sin (  θ )

                                  _______      =

                                        θ

 

 

9  *   1      =

 

 

9

 

 

cool cool cool

 Mar 2, 2019
 #3
avatar+18754 
+2

I actually like your way better.1...I just happened across l'Hopital and thought I would use it....    Thanx  !  ~EP

ElectricPavlov  Mar 2, 2019
 #4
avatar+102417 
0

Eh.....L'Hopitals  is just as good....and probably more "compact"

 

Like I always say.....there may be many roads that lead to the same destination !!!!

 

cool cool cool

CPhill  Mar 2, 2019

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