Recent content by SirPlus

With respect to time...

Homework Statement Derive the equilibrium state of a simple harmonic oscillation and show that the derivative of the maximum displacement is s^{'} = 2 \sqrt{E} Homework Equations F = -k x The Attempt at a Solution m a = -k s \rightarrow ms^{''}...

Homework Statement 1.Determine the divergence/convergence of the following improper integrals by the evaluation of the limit: \int_{0}^{∞} \frac{dx}{e^{-x} + e^{x}} Homework Equations The Attempt at a Solution Let u = e^x ∴ du = e^x dx I ended up with...

So how do i solve (a), where do i begin?

1. Homework Statement [/b] Use the direct comparison test to show that the following are convergent: (a)\int_1^∞ \frac{cos x\,dx}{x^2} I don't know how to choose a smaller function that converges similar to the one above. The main problem is i don't know where to start. A simple...

Thanks tia89, ill provide the whole work out in the next question - I am new to the forum and I am not very good at inserting equations etc. Please understand ...

Homework Statement A spring is freely hanged on a ceiling. You attach a mass to the end of the spring and let the mass go. It falls down a distance of 49 cm and comes back to where it started. It contineous to oscillate in a simple harmonic motion going up and down - a total distance of 49...

I obtained the maximum speed using the principle of conservation of linear momentum, i took the first derivative of the postion function with respect to time and equated the initial velocity at time zero - i then was able to determine the maximum displacement. Direction positive is along the...

Homework Statement A massless spring attached to a wall lies on a frictionless table. It has a block of mass 2kg attached to one end, initially the block is at rest. Another block, also of mass 2kg is sliding on the table top with a speed 8m/s. At t = o the moving block collides with the...

As an answer, would it be easier for me to rather tabulate values of x between zero and one for functions in numerator and denomenator to observe the trend? perhaps maybe sketch the graph for support - i guess its difficult to find the limit arithmetically

I don't get your argument vahess71 - i understand that as the x values decrease to the right the numerator as function tends to (- infinity) however the dinomenator tends to zero, the limit does not exist at all?

I got 1/0 ...

Hi, Find the limit of the function x^(1/x) as x tends to zero I had assigned y to x^(1/x) and took the natural logarithm on both sides but that had not given me a quotient in its indetermined form that is 0/0 or infinity / infinity maybe there is another approach not l'Hopitals rule ...

Thanks so we use vector notation, thanks pretty clear now ...

Sure, but doesn't tell me anything about the orientation of the force in a three dimensional space?