Find the limit

Question

limit as x approaches 0 (8/(xcot5x))

Answer 1

Hi Raj,

 

8/xcot5x <=> 8/[xcos(5x)/sin(5x)] <=> 8sin(5x)/xcos(5x) multiply top and bottom by 5

 

[8*5/cos(5x)][sin(5x)/x]  

 

sin(5x)/5x (as x approaches zero =1, let u=5x and you have (sin(u))/u which is equal to 1 as u----> 0 

 

cos (5x) as x approaches zero also is =1

 

=> 8/xcot5x (as x approaches 0) = 40