I am asked to compute the limit of the function $(\cos x-1)/(x^2)$, as $x$ tends to $0$, without using L'Hospital. The only thing I am aware of in this case that I have (0/0) is to use DLH and so I found that the result is -1/2. But I am asked to compute it without L'Hospital.I would appreciate of your guidance.
Asked
Active
Viewed 17 times
0
-
1hint: $$1-\cos x=2\sin^2 (x/2)$$ – Albus Dumbledore Nov 29 '20 at 11:59
-
Thank you very much! – Vasilis Nov 29 '20 at 12:02
-
Re Albus Dumbledore's comment, there are only 3 ways that I can think of to attack this problem (1) L'Hopital's rule (2) $\lim_{x\to 0} \frac{\sin x}{x}$ is known to equal 1 (3) Taylor series. – user2661923 Nov 29 '20 at 12:03
-
Thank you very much! – Vasilis Nov 29 '20 at 12:04