Recent content by vertciel

Thank you for your response, Mark44. Could you please explain the red box?

Hello everyone, I'm posting here since I'm only having trouble with an intermediate step in proving that \sqrt{x} \text{ is uniformly continuous on } [0, \infty] . By definition, |x - x_0| < ε^2 \Longleftrightarrow -ε^2 < x - x_0 < ε^2 \Longleftrightarrow -ε^2 + x_0 < x < ε^2 + x_0 1...

Dear all, Although the following question involves some terms using finance, I post it here since it seems to involve some probability. I hope that it will be fine. Thank you very much for your help. --------------------- Problem: Suppose that John buys shares in only one company...

Thanks for your response, rock.freak667. I have done some work, shown below, and have arrived at the correct answer. However, could someone please explain the formula v = rω ? How can I see this formula intuitively (especially since I have little background in physics)? Thank you...

Homework Statement *Please note that the following question is for a reasoning/thinking skills test. As I have only studied physics up to junior year in high school (and did not study pulleys then), I am unsure of the depth of physics knowledge required in this question, though it seems to...

Hello everyone, I have tried to write a proof based on HallsofIvy's response, posted below. However, I am not able to derive a contradiction from what I have at the moment. Could someone please assist me with the conclusion of this proof? Thank you very much. Attempt...

Thank you for your responses, Bohrok and HallsofIvy. @HallsofIvy: Thanks for your clarification on conjugates. How would you define a real conjugate then? Are two terms x and y conjugates of each other if and only x \times y are of degree 1 and do not have any fractional exponents?

Homework Statement Evaluate the limit, WITHOUT using l'Hôpital's rule: \lim_{x \rightarrow -1} \frac{x^{1/3} + 1}{x^{1/5} + 1} Homework Equations The Attempt at a Solution I tried to use the conjugate method which does not produce a useful outcome: \underset{x\to...

Thank you very much for your replies, Tedjn and Bohrok. I was able to evaluate this limit.

Homework Statement [B]Evaluate \underset{x\to 0}{\mathop{\lim }}\,\frac{\sec \frac{x}{2}-1}{x\sin x} , WITHOUT using l'Hôpital's rule. Homework Equations The Attempt at a Solution Hello there, I tried to evaluate this limit using two different approaches, both of which still...

Adminstrator: This is a double post, so please feel free to delete this one. The relevant post is "Limit of a Trigonometric Function (Involved Problem)". Homework Statement Evaluate \underset{x\to 0}{\mathop{\lim }}\,\frac{\sec \frac{x}{2}-1}{x\sin x} Homework Equations The Attempt at a...

Hi Bohrok, I'm just evaluating this limit for fun. Could you please reveal the last substitution which you made to get \frac{\sin x}{x} ? Thanks.

Thanks for your response, Hurkyl. Proof that \lim_{x \rightarrow 0} \frac{1}{x} does not exist: \lim_{x \rightarrow 0^{-}} \frac{1}{x} = \frac{1}{0^{-}} = -\infty \lim_{x \rightarrow 0^{+}} \frac{1}{x} = \frac{1}{0^{+}} = \infty Since the right- and left-sided limits differ and...

Thank you for your response, Hurkyl. However, how would I show with an assumed delta value that the above limit does not exist?

Hello there, I would like to learn how I can use the formal definition of a limit to prove that a limit does not exist. Unfortunately, my textbook (by Salas) does not offer any worked examples involving the following type of limit so I am not sure what to do. I write below that delta = 1 would...