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anonymous
 5 years ago
Find an integer which is the limit of (1cosx)/x
as x goes to 0
anonymous
 5 years ago
Find an integer which is the limit of (1cosx)/x as x goes to 0

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can use the sandwitch thm

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or you can do L'Hospitals rule

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0hopitals rule was my thought :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you take derivative of both top and bottom you'll get sin(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so as x>0, sin(x)>0 so the answer is 0

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can always do the long version :) 1cos(x+h)  1 + cos(x)  maybe? h

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you all. it's 0 as yuki said hehe

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its always been 0 lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is you use the sandwich thm \[1 \le \cos(x) \le 1 \] \[1 \ge \cos(x) \ge 1\] \[2 \ge 1\cos(x) \ge 0\] \[{2 \over x } \ge {1\cos(x) \over x} \ge 0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now if you take the limit on both sides \[\lim_{x \rightarrow 0} {2 \over x} \ge \lim_{x \rightarrow 0}{1\cos(x) \over x} \ge \lim_{x \rightarrow 0}{0}\] \[0 \ge \lim_{x \rightarrow 0}{1\cos(x) \over x} \ge 0\] so the limit is 0
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