OpenStudy (anonymous):

Hi. In lecture 3, in the derivation of the limit of (1-cos Θ)/Θ as Θ-->0 . I am able to understand tht the 'gap' 1-cosΘ nears 0 as Θ tends to zero. But then, doesnt it mean we re actually ending up with 0/0 rather than 0. can anyone clarify on this ?

6 years ago
OpenStudy (anonymous):

This is explained in Session 8 Course Notes Clip 3, Questions and Answers. Basically, as Θ tends to zero, the numerator (1-cos Θ) shrinks faster than the denominator Θ, giving a limit of 0. (Think of Θ as the length of the arc here).

6 years ago
OpenStudy (anonymous):

@alistair : thank you :) that helped :) clarified :)

6 years ago
OpenStudy (anonymous):

do one thing multiply and divide the whole limit \[(1-\cos \theta)\div \theta\] by an additional \[\theta\] then the read the limit as \[\lim_{\theta \rightarrow 0} ((1-\cos \theta)\div \theta ^{2}) \theta\] solve the limit as \[\lim_{\theta \rightarrow 0} ((1-\cos \theta)\div \theta ^{2}\] it'll come put to be 1/2 then the limit is left as \[\lim_{\theta \rightarrow 0} \theta\]*1/2 this is obviously equals to '0'

5 years ago