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  1. 5

    Second order non-linear differential equation involving log

    EDIT: my problem is solved, thank you to those who helped Homework Statement Solve: x y^{\prime \prime} = y^{\prime} \log (\frac{y^{\prime}}{x}) Note: This is the first part of an undergraduate applications course in differential equations. We were taught to solve second order...
  2. 5

    Compute the flux from left to right across a curve

    Homework Statement Compute the flux of \overrightarrow{F}(x,y) = (-y,x) from left to right across the curve that is the image of the path \overrightarrow{\gamma} : [0, \pi /2] \rightarrow \mathbb{R}^2, t \mapsto (t\cos(t), t\sin(t)). A (2-space) graph was actually given, and the problem...
  3. 5

    Use Lagrange multipliers to find the eigenvalues and eigenvectors of a matrix

    Homework Statement Use Lagrange multipliers to find the eigenvalues and eigenvectors of the matrix A=\begin{bmatrix}2 & 4\\4 & 8\end{bmatrix} Homework Equations ... The Attempt at a Solution The book deals with this as an exercise. From what I understand, it says to consider...
  4. 5

    Expressing geometrically the nth roots of a complex number on a circle

    Homework Statement Let z \in \mathbb{C}. Prove that z^{1/n} can be expressed geometrically as n equally spaced points on the circle x^2 + y^2 = |z|^2, where |z|=|a+bi|=\sqrt{a^2 + b^2}, the modulus of z. Homework Equations // The Attempt at a Solution My problem is that I am...
  5. 5

    Third degree Taylor polynomial in two variables

    Homework Statement Find the third degree Taylor polynomial about the origin of f(x,y) = \frac{\cos(x)}{1+xy} Homework Equations The Attempt at a Solution From my ventures on the Internet, this is my attempt: I see that \cos(x) = 1 - \frac{1}{2}x^2 + \frac{1}{4!}x^4 - \cdots...
  6. 5

    Solve sin(2x) dx + cos(3y) dy = 0, where y(pi/2) = pi/3

    Homework Statement Solve the equation \sin(2x) dx + cos(3y) dy = 0, where y(\pi/2) = \pi/3 Homework Equations N/A The Attempt at a Solution I understand the process that gets from the original equation to y = \frac{\arcsin(\frac{3}{2} (\cos(2x) + 1))}{3} However, I don't understand why...
  7. 5

    Confusion with probability models and intersection of events

    Homework Statement I will use an example to showcase my confusion: Suppose a person watches show A 2/3 of the time, show B 1/2 of the time, and both show A and show B 1/3 of the time. For a randomly selected day, what is the probability that the person watches only show A? For a randomly...
  8. 5

    The Limit of a Root of a Function is the Root of that Limit (delta-epsilon)

    Homework Statement Prove: If \lim_{x \rightarrow a} f \left( x \right) = l , then, if \sqrt[n]{f \left( x \right)} exists, \lim_{x \rightarrow a} \sqrt[n]{f \left( x \right)} = \sqrt[n]{l} . Homework Equations Nothing really... The Attempt at a Solution Okay, so here goes...
  9. 5

    Prove that Any Cubed Function is Differentiable (delta-epsilon method)

    Homework Statement Prove that: Any function f such that f(x)=x^3 for any x \in R is differentiable. Homework Equations Skip. The Attempt at a Solution Okay! So, to conclude, it must be shown that, for any a in the domain of f , \displaystyle \exists \lim_{h...
  10. 5

    Wire cut to shape circle and square so total area is maximum or minimum

    Homework Statement A piece of wire 40 cm long is cut into two pieces. One piece is bent into the shape of a square and the other is bent into the shape of a circle. How should the wire be cut so that the total area enclosed is a (a) maximum and (b) minimum? Homework Equations Area...
  11. 5

    Solving an equation with an absolute value within an absolute value

    Homework Statement Solve the equation | | 3x + 1 | - x | = 2 Homework Equations |x| = x if x \geq 0 |x| = -x if x < 0 The Attempt at a Solution To start, I have never dealt with such an equation before, and am partly 'iffy' with absolute values in general, but, up...
  12. 5

    Find the four points at which two lines are tangent to both parabolas

    Homework Statement Draw a diagram to show that there are two lines tangent to both of the parabolas y = - x^{2} (1) and y = 4 + x^{2} (2) Find the coordinates of the four points at which these tangents touch the parabolas. Homework Equations y - y_{o} = m(x - x_{o}) The Attempt at a...
  13. 5

    Simplifying the Derivative of the Square Root of a Sum Containing a Square Root

    Homework Statement EDIT: Ahhh, my apologies. At first, I thought it appropriate for the non-calculus sub-forum, but by the title it really does not, XD. I also can't seem to find how to remove it. The question really does not require calculus, though! Basically, the problem of finding the...
  14. 5

    Prove Power Rule by Math Induction and Product Rule

    Homework Statement Use the Principle of Mathematical Induction and the Product Rule to prove the Power Rule when n is a positive integer. Homework Equations Dxxn = nxn-1 Dx(fg) = fDxg + Dxfg The Attempt at a Solution In summary, Dxxn = nxn-1 Dxxk = kxk-1 Dxxk+1 = (k+1)x(k+1)-1 Dx(xkx) =...
  15. 5

    What is wrong with the following calculation using infinite series?

    Homework Statement What is wrong with the following calculation using infinite series? 0 = 0 + 0 + 0 + ... 0 = (1 - 1) + (1 - 1) + (1 - 1) + ... 0 = 1 - 1 + 1 - 1 + 1 - 1 + ... 0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + ... 0 = 1 + 0 + 0 + 0 + ... 0 = 1 Homework Equations None...
  16. 5

    Find an expression for the nth partial sum using this identity

    Homework Statement The series, 1 / (1 x 2) + 1 / (2 x 3) + 1 / (3 x 4) + ... + 1 / [n(n + 1)] + ... is not a geometric series. (A) Use the identity 1 / [k(k + 1)] = 1 / k - 1 / (k + 1) to find an expression for the nth partial sum Sn and (B) use it to find the sum of the...
  17. 5

    Becoming a Teacher: Specialist or Two Majors?

    Hello, I will be beginning my first year of university in the upcoming September, where I am enrolled in Concurrent Teacher Education/Science-Mathematics (in essence, it is a 5-year program, 4 of which is a B.A. or B.Sc. and 1 is the B.Ed. [teacher's college]). So, I am preparing my timetable...
  18. 5

    Charge to Mass Ratio of a Particle to Electron - Mass

    Homework Statement To start, I did find a few very similar or equal topics, but I could not gather enough information. And, the pi symbols are intended to be pi symbols with negative superscripts (couldn't get it to work/finalize). --- The charge-to-mass ratio of a \pi- particle is known to...
  19. 5

    Photoelectric Effect: Photoelectron Kinetic Energy vs. Frequency Graph

    Homework Statement A graph displays the kinetic energy of photoelectrons as a function of frequency of light falling on a cathode in a photoelectric cell. If the cathode is replaced with one of greater force of attraction to its electrons, describe how a graph of kinetic energy against...
  20. 5

    How Far is the 4th Maximum from the Central Maximum?

    Homework Statement How far would the fourth maximum be from the central maximum, provided the distance between maxima is 6. \times 10^{-3} m and this is double-slit light interference? Homework Equations See solution. The Attempt at a Solution It is known that the central maximum in...
  21. 5

    Preview Post Results in Post Data Duplication and Errors?

    Hello, I am using Internet Explorer 9. The following has occurred for Internet Explorer 8. When I attempt to preview a post or reply with Latex data inside, all is usually okay. But, when I make a change to the Latex, then preview post for a second time, the Latex data does not completely...
  22. 5

    What is the force required and amount of work done to stop this motion?

    Homework Statement An object of mass 1200 kg rests at a height of 95 m above the ground on a roller coaster. After a series of inclined planes, repeately reaching a height of zero, (bumps and drops of the roller coaster) the roller coaster lays horizontal on the ground (height zero) for 7 m...
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