# Search results

2. ### I Current in an RL-Circuit

Why is initial current zero in an RL ciruit with an emf, but it is not in a charging RC circuit?

4. ### Relativity of Length

a) We use the definition of speed: v = delta_L/delta_t delta_t = delta_L/v = 45000 m/(0.99540*3*10^8 m/s) = 1.55*10^-4 s b) We use the length contraction equation: delta_L = L_0*sqrt(1-v^2/c^2) L_0 = delta_L/sqrt(1-v^2/c^2) = 45000 m/sqrt(1-0.99540^2) = 469698 m However, the solution shows...
5. ### Solving the Integral ∫dx/(1-x)

I solved the integral by two different methods and I get different answers. Method 1: ∫dx/(1-x) = -∫-dx/(1-x), u=1-x, du=-dx ∫dx/(1-x) = -∫du/u = -ln|u| = -ln|1-x| Method 2: ∫-dx/(x-1) = -∫dx/(x-1), u=x-1, du=dx ∫-dx/(x-1) = -∫du/u = -ln|u| = -ln|x-1| What am I doing wrong?
6. ### Convergence of a Power Series

We transform the series into a power series by a change of variable: y = √(x2+1) We have the following after substituting: ∑(2nyn/(3n+n3)) We use the ratio test: ρn = |(2n+1yn+1/(3n+1+(n+1)3)/(2nyn/(3n+n3)| = |(3n+n3)2y/(3n+1+(n+1)3)| ρ = |(3∞+∞3)2y/(3∞+1+(∞+1)3)| = |2y| |2y| < 1 |y| = 1/2...

8. ### Find the interval of convergence of this power series

∑((√(x2+1))n22/(3n+n3)) We use the ratio test: ρn = |2(3n+n3)√(x2+1)/(3n+1+(n+1)3)| ρ = |2√(x2+1)| ρ < 1 |2√(x2+1)| < 1 No "x" satisfies this expression, so I conclude the series doesn't converge for any "x". However the answer in the book says the series converges for |x| < √(5)/2. What am...

10. ### Find the Interval of Convergence of this Power Series: ∑(x^2n/(2^nn^2))

∑(x2n/(2nn2)) We use the ratio test: ρn = |(x2n2/(2(n+1)2)| ρ = |x2/2| ρ < 1 |x2| < 2 |x| = √(2) We investigate the endpoints: x = 2: ∑(4n/(2nn2) = ∑(2n/n2)) We use the preliminary test: limn→∞ 2n/n2 = ∞ Since the numerator is greater than the denominator. Therefore, x = 2 shouldn't be...
11. ### Studying Self-Studying Physics

Hi Bill. I forgot to tell you that someone suggested me to start reading Analytical Mechanics (written by Fowles). I read it, but I didn't understand the last two chapters (Lagrangian Mechanics and Dynamics of Oscillating Systems), I guess the problem was calculus of variations. Then I tried to...
12. ### Studying Self-Studying Physics

Hi Bill. I forgot to tell you that someone suggested me to start reading Analytical Mechanics (written by Fowles). I read it, but I didn't understand the last two chapters (Lagrangian Mechanics and Dynamics of Oscillating Systems), I guess the problem was calculus of variations. Then I tried to...
13. ### Studying Self-Studying Physics

Hi Bill. I just feel kind of weak in math, so I started reading Boas from the beginning and I am almost done with the first chapter. Do you think it is okey if I start reading Landau once I am done with Boas? Thanks Fernando
14. ### Infinite Series (The Ratio Test)

Thank you for your response. I see my mistake now.
15. ### Infinite Series (The Ratio Test)

Shouldn't it be (2n +1) instead of (2n+2)?
16. ### Infinite Series (The Ratio Test)

I found that ρn = √(2n+1)/(n+1). Then, I found ρ = lim when n→∞ |(1/n) (√(2n+1))/((1/n) (n+1))| = 0 Based on this result I concluded the series converges; however, the book answer says it diverges. What am I doing wrong?

19. ### Infinite Series (Integral Test)

After evaluating the integral I found the following: (1/3)tan-1(e∞/3) = (1/3)tan-1(∞) = (1/3)(nπ/2), where n is an odd number. In this case I found multiple solutions to the problem. How do you prove it converges?
20. ### Infinite Series (Integral Test)

I got the following expression: -(1/4)ln((n+2)/(n-2)) When I substitute "∞" in the expression I found it undefined. However, the book says the series converges. What am I doing wrong?
21. ### Limits of Sequences

Thank you all for your responses.
22. ### Limits of Sequences

If n is ∞, then ln (n) = ln (∞) = ∞ Then, 1/∞ = 0 Any number raised to "0" = 1, so the answer should be 1. However the book says the answer is e2. Could you provide me some help?
23. ### Path Followed by a Light Ray

Got it! Thank you for your help.
24. ### Path Followed by a Light Ray

This is an example from a textbook. They show the following: ∫nds = ∫r-2*ds = ∫r-2*√((dr)2+r2*(dθ)2) How do you obtain the expression for ds?
25. ### How did Newton obtain F = ma?

What was the original experiment used to show that f = ma. What was measured in this experiment and how was it measured?
26. ### I How was F = ma obtained?

Thank you for your reply. So, in the experiment what was measured and how was it measured?
27. ### I How was F = ma obtained?

How was F = ma obtained? What is mass? If you say mass is amount of matter, then what is matter? How did they measure accelerations at that time?
28. ### Find the Euler Equation

You are totally right. I don't know why I didn't notice that before. Thanks a lot.
29. ### Find the Euler Equation

I start with the following: d/dx(dF/dy')-dF/dy=0 d/dx(d/dy'(y'^2+y^2))-d/dy(y'^2+y^2)=0 d/dx(2y')-2y=0 2d/dx(y')-2y=0 d/dx(y')-y=0 First path and the one found in the solution: y''=y Second path: ∫d(y')=∫ydx y'=xy+C What is wrong with the second path?
30. ### Find the Euler Equation

∫(y'^2+y^2)dx Why I obtain two different equations? 1. y''=y 2. y'-xy+C=0