# Recent content by Fernando Rios

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)?