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Yep that fixes it, I also made an algebraic error thinking sin was on the denominator. Brain is going to mush. Thanks!

Don't know why I said 'alternating' series in the thread title...my brain is becoming mush!

Homework Statement Sorry I don't know how to use symbols on this site so bear with me: the question is does the following series converge: sum of sin(1/n^2) where n goes from 1 to infinity Homework Equations Limit comparison test, maybe others The Attempt at a Solution Okay I think I got...

No, what are those?

Okay this problem might be over my head. I've only just learned first order linear differential equations and solving them by separation of variables. Is there any easier way to do this?

Yes. Check out riemann sums. You take the limits of areas of rectangles under the curve as the number of rectangles approaches infinity.

Homework Statement Find the solution to (x+1)y' +2y -(x+1)^(5/2)=0 Homework Equations Definiton of antiderivative The Attempt at a Solution I have been trying to manipulate this equation in every possible way so that I can get x on one side and y on the other. Ever attempt has...

Nevermind I figured it out. Problems solved.

Sorry one more question, how would you deal with finding the derivative if there was another function being multiplied by the integral? For example, d(x^5 * integral of f(x) from x to x^2-x)/dx? Do you use the product rule here or is there some other trick?

Thanks a lot!

Homework Statement I'm trying to solve a problem where you are asked to find the derivative of an integral where both limits of integrations contain variables Homework Equations Definition of integrals, derivatives The Attempt at a Solution For problems where you have an...

Homework Statement The problem: Find the derivative of x2 multiplied by the integral of dt/(t-2t2) from x to -x2+2x i.e, the function is x^2 times integral of [1/(t-2t^2)]dt from a to b with a being x and b being -x^2+2x Homework Equations Derivative and integral definitions The Attempt...

Sorry i was given dy/dx and was asked to solve for y, i just replaced with with f(x) and dy/dx with f'(x). The solution was to separate the variables, I forgot all about it.

Thanks again micromass

Homework Statement f'(x)= x+1-yx-y Solve for f(x) Homework Equations definitions of integrals and derivatives The Attempt at a Solution Okay, so I integrated both sides. This gives f(x) = x^2/2 + x -integral(yx) - integral(y) +c The problem I'm having is how do you...

That's much better, thanks for the help.

Homework Statement Graph x^(1/3) +x^(4/3) Homework Equations Limits, derivatives, etc. The Attempt at a Solution Hi guys, I was attempting this problem and then verifying it using a function grapher online. I noticed that all of the function graphers do not plot the function...

Okay that makes sense. Thanks for the help

Oh is is actually this easy? In that case, I would think since the numerator will always be positive regardless of which side the limit approaches from, and the denominator will switch signs depending on which side it approaches from, then the limit from the left will be -infinity and will be...

Homework Statement Calculate the limit as x-->pi/4 of [tan(x-pi/4)+1]/x-pi/4 Homework Equations lim h-->0 of [f(x+h)-f(x)]/h = f'(x) lim x--->a [f(x)-f(a)]/(x-a) = f'(x) The Attempt at a Solution I've attempted to turn this equation into the form f(x)-f(a)/x-a by letting...

Yes, that did it. Thanks a lot.

Homework Statement Find derivative of x^(2/3) from first principles (i.e limit definition) Homework Equations lim h-->0 (f(x+h)-f(x)/h) The Attempt at a Solution [(x+h)^(2/3)-x^(2/3)]/h I've tried multiplying the top and bottom by the conjugate, but I end up with the same...