Recent content by demersal

Yes, thank you very much. I think I can work it out now!

Homework Statement (1 pt) Compute the 9th derivative of: f(x) = \frac{cos(6x^4)-1}{x^7} at x=0. Homework Equations Hint: Use the MacLaurin series for f(x). The Attempt at a Solution I have tried many weird ways and cannot come up with the correct numerical answer. I've...

Homework Statement Find the area of the region enclosed by the asteroid: x=a*cos^{3}\theta y=a*sin^{3}\theta Homework Equations A = \int\sqrt{\frac{dy}{d\theta}^{2}}+\frac{dx}{d\theta}^{2}The Attempt at a Solution \frac{dy}{d\theta} = 3asin^{2}\theta(cos\theta) \frac{dx}{d\theta} =...

Ok, that sounds like a good idea. But I'm having trouble wrapping my head conceptually around the two square roots, since y^2 equals a term with a square root already in it. And does c go under the root? This may seem kind of trivial but I think this is why I've gotten this problem wrong 10...

Homework Statement Solve the separable differential equation Subject to the initial condition y(0) = -10: 7x-3y\sqrt{x^{2}+1}\frac{dy}{dx} = 0 Homework Equations Differential Equations The Attempt at a Solution I got up to the point where: -\frac{3}{2}y^{2}=-7\sqrt{x^{2}+1}+C...

I got: [(3-c)x^2+x-c] / [3x^3+x^2+3x+1] And then if I plug in for 3=c, I get lim as t approaches infinity of \int^{t}_{0} \frac{x-3}{3x^3+x^2+3x+1} And now, as my luck would have it, I am stuck integrating. I cannot factor the denominator so I think integration by parts is out of the...

Ahh, ok, I see what you mean by cancellation now. So I am basically trying to cancel out the effect of a smaller power of x over a larger power of x. But I'm not seeing a way to get rid of the x^3. Unless I am supposed to make the whole numerator 1? (I'm sorry I'm being so dense today...

Ok, I will try that, but I am still unsure of my objective in integrating. Should I be looking to eliminate factors from the top and bottom to simplify the integrand before I integrate and take the limit? And I am just looking to make it so that the limit exists?

Homework Statement Find the value of the constant C for which the following integral converges. Evaluate the integral for this value of C: \int \frac{x}{x^2+1} - \frac{C}{3x+1}dx from 0 to infinity Homework Equations The Attempt at a Solution \stackrel{lim}{t->inf.} \int \frac{x}{x^2+1} dx...

Oh, ok, I misinterpreted your original statement. Thank you for your help!

I completely understand now, thank you! Just one last question ... how does t -> infinity correspond to theta -> pi/2? I don't see how I could just plug infinity into sqrt(x^2-4) or something

If I do it that way, I get the answer as pi/4 and that is the end of it. I checked the answer online and it said the answer to the larger limit was 0, not pi/4. Am I neglecting something by just plugging in pi/2 for t?

Homework Statement \int \frac{dx}{x\sqrt{x^2-4}} from 2 to infinity Homework Equations Trigonometric substitution, improper integrals The Attempt at a Solution \int \frac{dx}{x\sqrt{x^2-4}} from 2 to infinity = \underbrace{lim}_{t->inf} \int \frac{dx}{x\sqrt{x^2-4}} from 2...

I am still trying to play with the formatting, sorry, I will write it out in words in the mean time: the integral of x over (x^2+2)^2 dx. But, yes, it seems like that simple u-substitution will work! Thank you ... I feel so silly for overcomplicating the problem!

Homework Statement \int\frac{x}{(x^2+2)(x^2+2)} dx from 0 to infinityHomework Equations Improper integralsThe Attempt at a Solution Lim_{t->\infty} \int\frac{t}{0} (\frac{x}{(x^2+2)(x^2+2)}) I tried integrating this by parts and also by partial fractions but neither seemed to lend itself...