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  1. C

    Alternating Series Question

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

    Alternating Series Question

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

    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...
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    Differential Equation

    No, what are those?
  5. C

    Differential Equation

    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?
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    Is there a general way to solve integrals?

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

    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...
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    Definite integrals

    Nevermind I figured it out. Problems solved.
  9. C

    Definite integrals

    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?
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    Definite integrals

    Thanks a lot!
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    Definite integrals

    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...
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    Derivative of a definite integral

    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...
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    Simple differential equation

    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.
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    Simple differential equation

    Thanks again micromass
  15. C

    Simple differential equation

    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...
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    Domain of a Function

    That's much better, thanks for the help.
  17. C

    Domain of a Function

    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...
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    Limit Calculation

    Okay that makes sense. Thanks for the help
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    Limit Calculation

    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...
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    Limit Calculation

    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...
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    Help with derivative

    Yes, that did it. Thanks a lot.
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    Help with derivative

    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...
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