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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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) =...
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...
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...
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...
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...
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...
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...
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...