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  1. J

    Easy stuff, i'm just retarded

    Well you know that by the properties of integrals, you can treat it as two integrals I=I_1+I_2=\left(\int 1dt\right)+\left(-\int\cos{t}dt\right) Do you know these integrals? What is the derivative of -\sin{t}?
  2. J

    Find the equation of the line of intersection of the planes:

    There are two parts two a problem like this. First you'll want to find the direction of the line of intersection, which is nothing but the cross product of the normal vectors of the planes, i.e. \mathbf{n_1}\times\mathbf{n_2}=\langle 2,-1,-1\rangle \times \langle 1,2,3\rangle. Then all you need...
  3. J

    Derivative Problem

    No problem. Watch out though, I think you have a sign error in there. f'(x)=-e-x+2e-2x=0 So then 2e-2x=e-x and therefore by dividing you get 2=e-x+2x
  4. J

    Derivative Problem

    Double check your derivative, you shouldn't be bringing an x down right? The derivative of ecx for a constant c is just cecx
  5. J

    Need help with differential eq. from book

    To solve differential equations in the form y'+P(x)y=Q(x) it is useful to use an integrating factor defined by \mu=\exp{\left(\int P(x)dx\right)} We multiply both sides of the equation by this, \mu y'+\mu P(x)y=\mu Q(x) and if you look closely the left hand side is the...
  6. J

    Laplace transform of sin(2t)cos(2t)

    Ah good--glad to help.
  7. J

    Laplace transform of sin(2t)cos(2t)

    Well if you have that \sin{(4t)}=2\sin{(2t)}\cos{(2t)} then \sin{(2t)}\cos{(2t)}=\frac{1}{2}\sin{(4t)} So then if you want to do it from the integral you just need to integrate \int_0^{\infty}\frac{1}{2}\sin{(4t)}e^{-st}dt where the s you treat as a constant (you're...
  8. J

    Laplace transform of sin(2t)cos(2t)

    Consider that \sin{(4t)}=2\sin{(2t)}\cos{(2t)}
  9. J

    Limit problem

    Have you tried anything yet? Where does the expression tend to as x goes to -1?
  10. J

    Using Laplace Transforms to solve IVP's

    You've pretty much finished it, all you need to recognize that Y(s)=\frac{s-1}{(s-1)^2+1} through completing the square in the denominator. Now can you get that to work with f(t)=L^{-1}\left\{\frac{s-a}{(s-a)^2+b^2} \right\} = e^{at}\cos{(bt)}
  11. J

    Max & Min

    You are right about the local max and min. For the second part--all an inflection point is, is where the second derivative (that which we use to determine concavity) is 0. So you would have f''(x)=2(x-2)+4(x+1)=0 Can you get it from there?
  12. J

    Differentiating a circle

    Usually with cases like this where it is inconvenient to differentiate explicitly you can use implicit differentiation.
  13. J

    Greens theorem-help setting up correct integral

    When you integrate a region, you do so on an interval x\in [a,b],y\in [c,d]. Does the integral make sense if a>b, c>d?
  14. J

    Greens theorem-help setting up correct integral

    It looks fine except I would check your order of limits--it should be entering at x=0 and leaving at x=y-2 and it's backwards for y too--maybe that was just a mistake when you wrote it.
  15. J

    Help whith fourier transform

    Oh ok I see what you're getting at--I haven't taken my complex analysis course yet, but that argument is very interesting.
  16. J

    Help whith fourier transform

    Don't go back to sin and cos it's much easier to deal with the exponential terms. Sorry I didn't mention it but it looks like they are Gaussian, you want to get it in the form \int_{-\infty}^{\infty}e^{-(x-a)^2} where this is a Gaussian integral centered at a. So you're dealing with right now...
  17. J

    Finding Maclaurin Series Expansions of Functions

    Yea it does take awhile; it looks like the first 4 non-zero terms are (it takes 21 terms to get them) 1-4x^7+10x^{14}-20x^{21} That looks like \sum a_n(-1)^nx^{7n} where the [itex]a_n[/tex] is some sequence that makes the {1,4,10,20,...}; I can't think of what would work for that at...
  18. J

    Finding Maclaurin Series Expansions of Functions

    Did you find the first 4 terms of the MacLaurin series for it yet? The idea is to look for a pattern in those to find the general form of the series.
  19. J

    Sum of Geometric Series

    Notice that 1-x+x^2-x^3+\ldots=\sum_{n=0}^{\infty}(-1)^nx^n=\sum_{n=0}^{\infty}(-x)^n
  20. J

    Inverse of This Laplace Function

    \frac{1}{(s^2+9)^2}=\frac{1}{s^2+3^2}\frac{1}{s^2+3^2} Can you make that a convolution of two inverse transforms you already know?
  21. J

    Find a vector parametrization for: y^2+2x^2-2x=10

    Well this basically looks like an off-center ellipse as you can see from the x term, so you'll want to parametrize it using the trig identity \cos^2x+\sin^2x=1 What happens if you complete the square on the x term and make it as such?... y=\sqrt{\frac{21}{2}}\sin{t}...
  22. J

    Tough Integral

    I think there is an error in your polynomial division if what you are meaning to say is that \frac{2x^3}{x^3-1}=2+2\frac{1}{x^{-1}}=2+2x The way that I would do it is to split up the integral like this.. \int\frac{2x^3}{x^3-1}dx=\int x \frac{2x^2}{x^3-1}dx=x\ln{(x^3-1)}-\int \ln{(x^3-1)}dx...
  23. J

    Help whith fourier transform

    Think of the cos term and the fact that \cos{\theta}=\frac{e^{i\theta}+e^{-i\theta}}{2} Then using that you should be able to solve the integral. \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\frac{e^{ix^2}+e^{-ix^2}}{2}e^{-ikx}dx
  24. J

    Help with an integral

    Yea I did it and got 0 because you end up integrating \cos(\theta)^3 at the end, which is 0.
  25. J

    First order differentials

    Yea it is non-linear I didn't notice that. What I said wont work.
  26. J

    First order differentials

    It looks like it is first-order homogeneous. Make the substitution z=x/t by dividing by t throughout your t/(2t+x), and then x=tz and x'=z+tz' by the product rule. Now it's in a form you want it for the relevant equations you listed. Just make the substitution the other way when you've solved for z.
  27. J

    Finding roots in an equation

    Have you learned the rational root test?
  28. J

    Column space

    Oh yea sorry I read your matrix backwards accidentally. Glad you got it.
  29. J

    Column space

    Your matrix A reduces to the identity matrix in reduced row echelon form; so then the column space is made up of all the columns of the original matrix; \text{Col}(A)=\left\{ \begin{pmatrix} 1 \\ -3 \end{pmatrix} , \begin{pmatrix} 2 \\ 5 \end{pmatrix} \right\} So does the vector they're...
  30. J

    Calculate the line Integral

    That would be the parametrization of the line y=x, but your curve that the line integral is over is the ellipse 4x^2+25y^2=100 \Rightarrow \text{ } \frac{2^2}{10^2}x^2+\frac{5^2}{10^2}y^2=1 I wrote it in a more suggestive way; can you see why the parametrization should be the...