Maxima Definition and 162 Threads

Homework Statement A uniform rod of mass M and length L can rotate around point P which is at position x from one end of the rod as shown in the figure. The rod is gently placed on a rough horizontal surface that has a friction coefficient μ. and at t=0 starts rotating with angular velocity...

I am clueless. Here's the model I tried to follow: g(a):=a^2-1; f(a,b):=a+g(a)-b; f(a,b); With output −b+a^2+a−1 Which is 1)Define a function in terms of some variable(s). 2)Define another function in terms of some variable(s) and in terms of the function defined in 1). 3)Evaluate the function...

Hi guys, I've used google and Maxima's manual but couldn't find what I'm looking for. I have defined a function similar to Z(beta):=beta+3;, and another function P(beta):=beta+7/Z; and I am not able to "simplify" P(beta) as beta+7/(beta+3). I've tried several commands but all failed. I even...

Homework Statement A thin hair is placed between two microscope slides. When laser light is shined down onto the slides, periodic intensity maxima are seen to span the slides. Which of the following changes will decrease the distance between the maxima? I. Decrease the wavelength of the laser...

Homework Statement Consider the differential equation y'=x-y^2. Find maxima, minima and critical points; show that for every solution f=f(t) exists T\geq 0 such that f(t)< \sqrt{T}\;\forall t > T Homework Equations The Riccati equation: y'=a(x)y^2+b(x)y+c(x) The Bernoulli equation...

Could someone walk me through how to maximize this 2-variable function wrt z? http://www.wolframalpha.com/input/?i=z+%3D100%2F%281%2B%28root+%28%28x-2%29%5E2+%2B+%28y-3%29%5E2%29%29%29+-+100%2F%281%2B%28root+%28%28x-2%29%5E2+%2B+%28y-3%29%5E2%29%29%5E2%29 I know the set of solutions will...

Hey! :o I am looking at the Gibbs Phenomenon for the function $\displaystyle{f(x)=sgn(x), x \in [-\pi, \pi]}$. The Fourier series of this function is: $$sgn(x) \sim s(x)=\sum_{k=1}^{\infty} \frac{4}{(2k-1) \pi} \sin{((2k-1)x)}$$ Since $f$ is odd, it's sufficient to look its behaviour at $[0...

A rectangle with length L and width W is cut into four smaller rectangles by two lines parallel to the sides. Find the maximum and minimum values of the sum of the squares of the areas of the smaller rectangles. Unless I did incorrectly, the algebra is very very long... HELP

Homework Statement From Mary Boas: Math for Phys. Sci. Ch1.15.20 20. By computer or tables, find the exact sum of each of the following series. a. \sum _{ n=1 }^{ \infty }{ \frac { { n } }{ { (4{ n }^{ 2 }-1) }^{ 2 } } } Homework Equations N/A. One is supposed to use an analytic...

Homework Statement A grating has 1070 lines per centimetre, and a flat screen is perpendicular to the ray that makes the central peak of the diffraction pattern. The screen is 3.20 m from the grating. If light of two wavelengths, 630 nm and 705 nm, passes through the grating, what is the...

Homework Statement microwave of wavelength 3 are incident to a row of parallel metal rods. The separation of the rods is 10cm. The first order diffraction is observed at 25° to the direction of the incident wave. Determine the angle between the first and the second order of diffraction maxima...

1. If f(x,y)=e^{x}(1-cos(y)) find critical points and classify them as local maxima, local minima, or saddle points. The Attempt at a Solution I found the partials and mixed partial for the second derivative test as follows: f_{x}=-e^{x}(cos(y)-1) f_{y}=e^{x}(sin(y))...

Homework Statement Consider the function f(x,y) = (x2 + 4y2)e(1-x2-y2) Find all critical points, and identify them as maxima, minima, or saddle points. The Attempt at a Solution I took the partial of x and the partial of y, and set them equal to 0. This is what I got: fx(x,y) =...

Homework Statement Find the maxima and minima of: f(x,y)=(1/2)*x^2 + g(y) g∈⊂ (δ⊂ ℝ ) in this region Ω={(x,y)∈ℝ2 / (1/2)*x^2 + y^2 ≤ 1 } hint: g: δ⊆ ℝ→ℝ The absolute min of f in Ω is 0 The absolute max of f in Ω is 1 Homework Equations The Attempt at a Solution I have the...

Homework Statement I have to find the relative maximum, so I'm going to set the second derivative to zero and solve. But, this is where I'm stuck. Homework Equations f"(x)= (x^2-4)(sin(2x)) - (2x)(1+cos^2(x))/ ((1+cos^2(x))^2) [The entire equation is divided by the ((1+cos^2(x))^2)] The...

Homework Statement I have been trying to find the value of x that maximizes the function is section 2. z is a variable distributed using a standard normal distribution i.e. can vary between -∞ and ∞, but generally is between -4 and 4. m varies between 0 and 1. c varies the same way as z. x...

Homework Statement A light of wavelength 500 nm interferes through a two slit experiment on a screen. The distance between the first minimum and fourth minimum is 1.68 cm. Find the distance between the central maximum and first order maximum.Homework Equations d*sin(θ) = nλ = Δ d = distance...

Hi Everbody, I am having a bit of trouble with an AS Physics question regarding diffraction gratings. I have managed to solve the problem that I have been facing, although I am not completely sure that I got to it through the correct means, and also why the answer is such. Homework...

Is it possible to get either one to display the less factored form of an expression? what I am doing is multiplying matrices together for geometrical optics but my answers keep coming out really ugly. For example I have d-d\left(\frac{2d}{r}-1\right) I don't think a person would ever write...

1. Problem: A manufacturer makes two models of an item, standard and deluxe. It costs $40 to manufacture the standard model, and $60 for the deluxe. A market research firm estimates that if the standard model is priced at x dollars, and the deluxe at y dollars, then the manufacturer will sell...

A point P whose x-coordinates is a is taken on the line y=3x-7. If Q is the point(4,1) show that PQ2 = 10a2-56a+80. Find the value of a which will make the expression a minimum. Hence show that the coordinates of N, the foot of the perpendicular from Q to the line are (24/5 , 1 2/5). Find...

hi pf, this is my 1st math question. i am a undergraduate grade 12 student and my question is what is the basic difference between local maxima minima & global maxima minima?

Here is a screenshot: http://i.imgur.com/AG3EL.png Does anyone know what I am doing wrong here? I'm used to Mathematica because it's more syntax-lax but I guess in Maxima it's more explicit and strict. I've looked at examples online and they seem no different than what I have input, so I...

My first post and I am new to forum etiquette, please go easy on me. I have an exam in a few days and have a good grasp on the content. Historically the professor has been putting harder Lagrange questions on the exam than are available in my textbook and supplement books or that I can find...

Homework Statement A corridor of with a is at right angles to a second corridor of width b. A long, thin, heavy rod is to be pushed along the floor from the first corridor into the second. What is the length of the longest rod that can get around the corner? Homework Equations I...

Homework Statement Locate all relative maxima, relative minima ,and saddle points if any. f(x,y)=ysinx fx(x,y)=ycosx fy(x,y)=sinx ycosx=0 sinx=0 y=0 x=0,∏,2∏... up until infinity Critical points at (0,0),(∏,0),(2∏,0)... fxx(x,y)=-ysinx...

Homework Statement Consider the following function of the variable r, r>/=0 y(r)=(r^(2)-5.50r)exp(-r) Find the value of the first derivative dy/dr at r=5.50 Homework Equations How do I solve this? I know its a simple derivative equation, but I can't seem to get it. I tried finding the...

Homework Statement Assume that the polynomial P(x) has exactly two local maxima and one local minimum, and that these are the only critical points of P(x). Sketch possible graphs of P(x) and use them to answer the following. (e) What is the sign of the leading coefficient of P(x)? positive...

The cycloid is defined by the parametric equations x = a(t-sin(t)) and y = a(1-cos(t)) I am trying to find the set of points of relative extrema of a cycloid. I differentiated first to get \frac{dx}{dt} = a(1-cos(t)) and \frac{dy}{dt} = a*sin(t) Then, by the chain rule...

Maxima word problem -- Not sure about my answer. This was in an assignment handed out after our introduction to extrema's. A builder wants to build a small building consisting of 4 walls and a roof (all rectangular). The cost of the bricks for the walls will be $25/square metre, while the roof...

Two waves of equal intensities "I" beat together, what is the maxima of the beat equal to ? Is it 0 or infinity,or other answers... I just couldn't get it

Here's the problem I'm trying to solve, We have an N dimensional surface. We do not know the form of this surface however we have datapoints which are likely to be close, though not guaranteed to be on the surface, with some outliers. What I want to do is determine where in N dimensional...

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. is this way correct? assume that x is side of square and r is radius of circle k=4x+2∏r sum of...

θHomework Statement Two gratings A and B have slits separations dA and dB, respectively. They are used with the same light and the same observation screen. When grating A is replaced with grating B, it is observed that the first-order maximum of A is exactly replaced by the second-order...

Could you pls advise me any reference (textbook for example) where I can find how to calculate maxima minima of function of several variables... or drop a couple of lines here.. Thank you

Homework Statement A lens with radius of curvature R sits on a flat glass plate and is illuminated from above by light with wavelength λ (see picture below). Circular interference patterns, Newton's Rings, are seen when viewed from above. They are associated with variable thickness d of the...

Hi, I have been going over past papers and i found this question. Find any local maxima or local minima of the functions g(x) = |f(x)| and h(x) = +√f(x) in the interval, −∞ < x < ∞. How Would I go about solving this?

Homework Statement I am given the problem "A function is defined by f(x) = 1-x^(2/3). a. find the minima and maxima of the function. State whether they are relative or absolute. b. graph the function." Homework Equations I found the derivative and set it equal to zero. y' =...

Homework Statement F(x)=(x^2)/(x+1) Find critical points Find local maxima & minima Homework Equations None The Attempt at a Solution F'(x) = x(x+2)/(x+1)^2 crit points: -2,0,-1 f(-2) = -4 f(0) = 0 f(-1)=undef My book is telling me that f(0) is the minima, and f(-2) is the...

Homework Statement ## f\left( x,y\right) =x^{2}-4xy+6x-8y+2y^{2}+10 ## ## f_{x}=2x-4y+6=0 ## ## f_{y}=-4x-8+4y=0 ## ## f_{y}=-4\left( x-y+2\right) ## -2=x-y, then solving fx and using this equality ## f_{x}=0=2\left( x-2y+3\right) =0 ## 2(-2 -y+3)=0 2(1-y)=0 y=1, then pluggin...

hi ! recently i just installed maxima on my ubuntu and it was installed and worked properly , until i managed to do some plotting. i have to change the default plot_format => gnuplot_pipes into openmath for the plot function executed nicely. problem solved for a while, until i figured out that...

The central maxima is of highest intensity and then the successive maximas keep reducing in intensity. Has it got something to do with increasing number of waves which sort of interefere (the word has not been used in the sense of intereference pattern but as a normal english word) with the...

1.Find the vertical and horizontal asymptotes (if any), intervals of increase and decrease, local maximum and minimum values, intervals of concavity and inflection points for f(x) = 1 / (L - x^1/2) 3. I found the vertical asymptote to be "x=0" , I found the horizontal asymptote to be "y=0" So...

For example, F(x) := x^2; Fx(x) := diff(F(x),x,1); didn't seem to work, since Fx(3); returned an error. Any help would be appreciated.

A laser emitting light with a wavelength of 560 nm is directed at a single slit, producing an interference pattern on a screen that is 3.0 m away. The central maximum is 5.0 cm wide. determine the width of the slit and the distance between adjacent maxima. attempt i used this equation...

Monochromatic light illuminates a pair of thin parallel slits at normal incidence, producing an interference pattern on a distant screen. The width of each slit is 1/7 the center-to-center distance between the slits. Which interference maxima are missing in the pattern on the screen? every...

Homework Statement I have attached the problem... Homework Equations dsin(\theta) = \lambdam The Attempt at a Solution (0.00003m)(sin(\theta)) = (0.000000550m)(2) ------------> 2.10o (0.00003m)(sin(\theta)) = (0.000000550m)(3) ------------> 3.15o I looked through my textbook...

Homework Statement A man holds a light that emits light of wavelength λ. The light beam passes though a pair of slits separated by a distance d, in a screen plate attached to the front of the light beam(double slits experiment). The beam then falls perpendicularly on a screen, getting an...

Dear all, In order to develop in cos in sin terms and then simplify the expression...

Homework Statement 3 narrow slits with spacing of d and 3d/2 as in picture, the slits are irradiated from left with a plane of monochromatic light with wavelength 2d/5. If the bottom slit is covered with a filter that introduces a half phase change, how many principal maxima will be...