+0  
 
+5
390
1
avatar+9 

hi everyone :)

how could I solve this :

 

WITHOUT USING L'HOSPITAL RULE :)

 

IM LOST :(

skcmarek  Oct 27, 2014

Best Answer 

 #1
avatar+26971 
+5

When x is very large pi/5x is very small.

 

When z is very small sin(z) → z, so when x is very large xsin(pi/5x) → x*pi/5x

 

5x increases much more rapidly than x, so x*pi/5x → 0

 

Hence, in the limit as x → ∞, xsin(pi/5x) → 0

.

Alan  Oct 27, 2014
 #1
avatar+26971 
+5
Best Answer

When x is very large pi/5x is very small.

 

When z is very small sin(z) → z, so when x is very large xsin(pi/5x) → x*pi/5x

 

5x increases much more rapidly than x, so x*pi/5x → 0

 

Hence, in the limit as x → ∞, xsin(pi/5x) → 0

.

Alan  Oct 27, 2014

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