anonymous
  • anonymous
Hello, In video lecture 3, Prof. Jerisson proved that limit of (1- cos theta)/theta as theta approaches 0 is 0. I understand why (1- cos theta) tend to 0. But what about theta itself in the denominator? As questioned by one student there, why didn't it become 0/0? I'm still confused. Anybody can explain further please?
OCW Scholar - Single Variable Calculus
jamiebookeater
  • jamiebookeater
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

phi
  • phi
Yes, the explanation was very "hand-wavy" The short answer is if you have a ratio of two things that "go to 0" *but* the top value goes to zero *faster*, then the ratio approaches zero. for example \( \frac{x^2}{x} \) when x=0.1, x^2 =0.01. when x=0.01, x^2= 0.0001, etc Of course we could simplify that to just x, and it evidently goes to zero... but the idea is still valid... the top and bottom can go to zero at different rates, and it is a race which wins.
phi
  • phi
For a specific argument see the attached file. For a clear explanation of the limit of sin x/ x you might want to see https://www.khanacademy.org/math/differential-calculus/limits_topic/squeeze_theorem/v/proof-lim-sin-x-x and for better background on limits, see http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-5-a-more-rigorous-approach-to-limits/
1 Attachment

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.