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Karo-lina-s [1.5K]
3 years ago
10

Lim x tanx/ 1-cosx x―>0 please help... ...?

Mathematics
1 answer:
lakkis [162]3 years ago
8 0
Note that 1 - cos(x) = 2sin²(x/2) 

⇒ lim x→0 xtan(x)/ [1 - cos(x)] = 

= lim x→0 xtan(x) / 2sin²(x/2) = 

= lim x→0 1/2 xtan(x) / [sin²(x/2) / (x/2)² * (x/2)²] 


Also, we know that lim x→0 sin(x)/x = lim x→0 tan(x)/x = 1 

So the limit is : 

= 1/2 lim x→0 xtan(x) / (x²/4) = 

= 1/2 lim x→0 4/x² * xtan(x) = 

= 2 lim x→0 tan(x)/x = 

<span>= 2.


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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