+0  
 
0
7
2
avatar+0 

Compute \(\lim_{\theta \rightarrow 0} \frac{1 - \cos\theta}{\theta}\)

 Feb 24, 2024
edited by wmath  Feb 24, 2024

Best Answer 

 #2
avatar+128406 
+1

Using l'Hopitals rule

 

lim     sin  θ  =    0

θ → 0   

 

 

cool cool cool 

 Feb 25, 2024
 #1
avatar+1370 
0

First, we can rewrite the numerator:

 

lim theta -> 0 (1 - cos theta)/theta = lim theta -> 0 2 sin(theta/2)^2/theta

 

We can then simplify and apply l'Hopital's Rule:

 

lim theta -> 0 2 sin(theta/2)^2/theta = lim theta ->0  4 sin (theta/2) cos(theta/2)/1 = 4.

 

Therefore, the limit is 4.

 Feb 25, 2024
 #2
avatar+128406 
+1
Best Answer

Using l'Hopitals rule

 

lim     sin  θ  =    0

θ → 0   

 

 

cool cool cool 

CPhill Feb 25, 2024

2 Online Users

avatar