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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...

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...

Hello there, Although there are oxygens on both sides of the equation, there are two on the left and three on the right. Therefore, you need to add one water molecule on the left for compensation. HNO2 + H2O -> NO3- Since you have three hydrogen atoms on the reactants' side, add three to the...

You're welcome. Unfortunately, I still have not found a different answer. Is this textbook a recognised, leading one in chemistry? If not, then the answer key may be erroneous.

Hello there, Unfortunately, I'm not an expert in the area of thermal physics. I have always interpreted Gibbs Free Energy as the amount of energy available to do work in a system. Does that help?

Hello there, I get the same answer in mol/(L x s) as you. Could you verify that the correct answer is given in the same units? Thanks.

Hello there, I am unsure about how your solution addressed this question, but this is what I would do. 1) You need to understand this equation: ∆G = nFE0cell. 2) You can calculate ∆G for the entire reaction using tabulated values of ∆G for each reactant. That is, ∆G for the reaction = ∆G...

Hello there, You are missing a key equation: mc∆T = -mc∆T, where ∆T = Tf - Ti. I encourage you to learn this equation and then retry the problem. If you need any more help, please write back!

Hello there, This can be considered as a "tricky" question. I did not arrive at the right answer on my first try. You have to read the question carefully. Although you calculated the standard OXIDATION potential for Pd -> Pd2+ + 2e- correctly, you are asked for this half-reaction's standard...

Hello there, I will start by writing the chemical equation: Mg + Cu(SO4)2 -> Cu + Mg(SO4)2 b) For this part, you know that Mg is in excess. Therefore, you simply need to find the amount of Cu(SO4)2 in mols. When you have this, then you know that the excess amount of Mg will be anything > the...

Thanks for your reply, Dick. I have: \vec{u} = |\vec{u}| \cos A1 \hat{i} + |\vec{u}| \cos B1 \hat{j} + |\vec{u}| \cos Y1 \hat{k} \vec{v} = |\vec{v}| \cos A2 \hat{i} + |\vec{v}| \cos B2 \hat{j} + |\vec{v}| \cos Y2 \hat{k} If I dot these two expressions on the RS, I do not see...

Could anyone please offer an explanation for how to prove the above? Thank you!

Homework Statement How many moles of solid sodium fluoride should be added to 1.0 L of a saturated solution of barium fluoride, BaF2, at 25OC to raise the fluoride concentration to 3.0 x 10-2 mol/L? The solubility product constant for BaF2 is Ksp = 1.7 x 10-6 at 25OC. The Attempt at a...

Thank you for your response. Would you mind elaborating on the proof? I thought that the direction cosines themselves were the unit vectors, so how would \cos A1 \cos A2 = 0 ? Shouldn't the dot product of these direction cosines = 0?

Hello everyone, Thank you in advance for your help! --- Homework Statement 10. A vector \vec{u} with direction angles A1, B1, and Y1, is perpendicular to a vector \vec{v} with direction angles A2, B2, and Y2. Prove that: \cos A1 \cos B2 + \cos B1 \cos B2 + \cos Y1 \cos Y2 = 0. ---...

Thank you for your response!

Homework Statement Calculate the work done when the volume of a cylinder is increased by 90.0 L against the atmospheric pressure. Think about the upward movement of a piston as it expands the volume of a cylinder. --- I am actually an AP Chemistry student and am supposed to do this...

Homework Statement 1. Explain why the following chemical reaction would not be effective to determine [Fe2+] in a given solution. Fe2+ (aq) + H2O2 (aq)-> Fe3+ (aq)+ H2O(l) | in acidic solution Homework Equations The Attempt at a Solution Hello: I am thinking that there may be a lack of...

Hello: Hydrogen is not a metal; it is a gas at room temperature. However, it has an unique chemical property. Like the alkali metals, it can lose its electron and just be a H+ proton (since it has no more electrons); or it can act like an halogen and gain an electron, to become H-. Hope...

Thanks for your reply, Kushal. Could you please explain how potassium perchlorate is an oxidising agent?

Hello: I am having some trouble relating to the following question to the concept of oxidation numbers as required by my practice problem, and would appreciate any help. Thank you! --- 1. Explain why it is dangerous to grind a mixture of Al with KClO4 in a mortar and pestle. ---...

Hello everyone: For the following problem, I arrived at the correct answer but am unsure about the method used. Could someone please check my work to see if it is legitimate or if it is a fluke? Thank you. --- 1. The age of wine can be determined by measuring the trace amount of radioactive...

Thank you very much for your help!

Thanks for your reply, Mike H. I apologise; I didn't realize that this was the correct forum. If someone could please move this to the Homework Help section, that would be appreciated. I have rewritten my work with units: k = 4.3E13 \frac{1}{s} \times e^{\cfrac{-103 \frac{kJ}{mol}}{8314...

Hello everyone, I am having trouble with determining where I erred in the following exercise. If someone could point out my mistake, I would appreciate the help. Thank you! --- 1. The decomposition of N2O5 has an activation energy of 103 kJ/mol and a frequency factor of 4.3E13 s^-1 . What...

Thanks for your reply, ygggdrasil. Does this exception occur often? If so, what would be the maximum number of valence electrons allowed for chlorine? 20?

Hello everyone: I was looking at Wikipedia's page on chloric acid (http://en.wikipedia.org/wiki/Chloric_acid) and was wondering if the Lewis diagram there is correct. I will not link directly to it as it has a high resolution. It shows Cl with a lone pair of electrons having double bonds with...

Hello there: Here is my solution, which matches your textbook's. y = \cos(a^3 + x^3) Let: u = a^3 + x^3 The Chain Rule: h'(x) = f'(g(x)) \times g'(x) Breaking the original equation down: f(x) = \cos u , f'(x) = -\sin u g(x) = u = a^3 + x^3 , g'(x) = 3x^2 (From the Product Rule)...

Thanks for your reply, dynamicsolo. However, I am looking in my textbook and it says that the general formula for length of an open air column (in both ends) in wavelengths is: L = \frac{\lambda}{2} . What may I be missing?

Hello there, For the following problem, I am arriving at an answer different from the given one so I would appreciate any help or hints. Thank you. My work is shown below. --- 1. A slightly smaller plastic pipe is inserted inside a second plastic pipe to produce an air column, open at both...

Thanks for your reply. However, his daughter is exerting friction on the entire toboggan. Wouldn't the father have to compensate for this by doing more work?

Hello everyone, I am having some trouble understanding why friction is not accounted for when calculating work done, as in the following two problems. If an object is experiencing friction, wouldn't there need to be more work done to continue moving the object? Thank you! --- 1. A father...

Hello there, I am trying to find the coefficient of friction for a rectangular wooden block. I have the force of friction but I do not know how to find the normal force. The weight of 1 block is 2N. Could someone please explain how I could find the normal force? Would I just multiply 2N by...

Hello everyone, For the following absolute value equations, I have no trouble solving them and finding the valid x solutions by plugging all the x solutions into the original equation. However, I am just wondering if could someone please show me how to set restrictions for the following...

Thank you for your replies, foxjwill and kurdt. I got the answers!

Thanks for your reply. The answers are: 1. a) 7.5 s b) 3.8 m/s 2. a) 15s

Thank you for your replies. @Foxjwill, so are you recommending me to use (v_2)^2 = (v_1)^2 + 2ad ? @Kurdt, are you recommending me to use displacement = (v_1)t + \frac{at^2}{t} ? Also, I tried to represent the sum of the distance of the two as such but I did not get the right answer...