Maxima Definition and 162 Threads

Homework Statement Light with a wavelength of 530 nm is incident on 2 slits that are spaced 1.0mm apart. If each slit has a width of .1mm, how many interference maxima lie within the central diffraction peak?Homework Equations sin( degree) = m(lambda)/d The Attempt at a Solution I have no...

Homework Statement Si(x) = \int_{0}^{x}{\frac{sin(t)}{t} dt At what values of x does this function have a local maximum? 2.Solutions [PLAIN]http://img833.imageshack.us/img833/701/27444263.png The Attempt at a Solution So I took the derivative and applying FTC and I got sin(x)/x = 0 sin(x)...

a problem in minima and maxima applicatios (urgent !)please Homework Statement A straight river 3km wide runs due east. A cable is to be laid from a point A on the south bank of the river to a point B on its north bank, 9km downstream from A. The cable is to be laid in a straight line from...

I am designing web software to interface to \LaTeX, Maxima and R. What I wanted to get feedback about is: 1) Security issues which may arise from calling Maxima and R from the web. The interface is going to be a AJAX GUI and not a raw command-line input form so I will be able to filter...

Hi there. I've got this function f(x,y)=(y-3x^2)(y-x^2), and I have to analyze what happens at (0,0) in terms of maxims and minims. But what I actually have to proof is that there's a saddle roof at that point. Theres is a critical point at (0,0). Let's see...

Homework Statement Show that the angular locations of the first to fourth secondary maximas are \alpha = a sin \Theta/\Lambda = 1.43030 2.45902 3.47089 4.46641 respectively. a is the slit width = 0.00016m \Lambda wavelength of laser 650nm Homework Equations I(\Theta) = I0...

URGENT! michelson interferometer - maxima and minima Homework Statement If a wave is reflected at a surface of a plate with higher refractive index (eg. At air glass or air-metal) it suffers a λ/2 phase change. Show that for the interferometer, maxima will occur for 2dcosθ = (n+1/2)λ and...

Homework Statement Hi there. I've got some doubts about the maxima and minima on this function: f(x,y)=x \sin y. I've looked for critical points, and there's only one at (0,0). The thing is that when I've evaluate the second derivatives I've found that f_{xx}=0, then I have not a defined...

Homework Statement Let An be the nth term of an A.P. and if A7 = 15, then the value of the c.d. that would make A3 x A7 x A12 greatest is : 1)9 2)9/4 3)3/8 4)18 Homework Equations The Attempt at a Solution Applying AM>=GM A3+A7+A12/3 >= (A3 x A7 x A12)^1/3 given that...

Homework Statement A farmer is planning to build six adjoining rectangular pens of equal size to house his hens, as shown in the diagram. He only has 180m of fencing, however, and he wants to make the pens as large as possible. Find the maximum area he could make each pen. The diagram is...

Homework Statement I do not have a specific homework problem, but could someone please clarify this for me? QUESTION: When you have an absolute maxima (or minima), how can you tell if it is ALSO a relative maxima (or minima)? I understand how to find absolute extrema on a closed...

Does a constant function have a local maximum?

Hey my problem is that I am unable to calculate the absolute value of the following function: f(z)=\bar{z}(z-2)-2\Re z wherase z=x+iy What i did was: =|z|^2-2\bar{z}-2\Re z=x^2+y^2-2x+2iy-2x=x^2+y^2+2yi-4x and how should i calculate the absoulte value of this function?? Because i should...

What effect does the distance between the two slits have on the intensity of the maxima?

Hello, everyone. Excuse me but I think I should post this question in sub-forum Calculus & Beyond Learning Materials but I can't access to that sub-forum and so... The question is: I began to learn to work with Maxima and I have several doubts. The help of the program is a little...

Homework Statement I calculated T_o to be 1.27 seconds and "T_o"' to be 1.23 seconds, each representing a normal mode of oscillation. These are correct according to the text. Here is the question: what is the time interval between successive maximum possible amplitudes of one pendulum after...

I'm wondering if anyone knows how, using the Maxima CAS, to force the evaluation of an expression? For example, if a function returns something like the following as a solution: -\frac{{2}^{\frac{6}{4\,log\left( 2\right) -5}+2}-5\,\left( \frac{6}{4\,log\left( 2\right) -5}+2\right) }{log\left(...

Homework Statement Find the maximum and minimum values of f(x,y) = (xy)2 on the domain x2 + y2 < 2. Be sure to indicate which is which Homework Equations I am not sure what to put here. I solved this problem a different way, and I am not confident I did it correctly. The Attempt at a...

Homework Statement Two slits are separated by 0.260 mm. A beam of 500 nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range -31.0° < θ < +31.0°. Homework Equations i used dsinθ = m(lambda) The Attempt at a...

Many of you are probably already familiar with the following phenomena: Many gtr-related questions in PF are often best answered using the result of some computation; for example, someone often incorrectly believes that the Einstein tensor of his manifold vanishes), Computations "by hand"...

I am new, but i have a question about the TI -89 Titanium calculator, does anyone how if i can plug in the equation f(x)=2x^3-15x^2+36x-1 to identify each location of the local maximun and minimum, and inflexion poits? Will this calculator do this?

Homework Statement Light of wavelength 680 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin θ = 0.2 and sin θ = 0.3, respectively. The fourth-order maxima are missing. (b) What is the smallest slit width this grating can have?Homework...

1. Find the absolute maxima and the absolute minima of the following function f(x)=(2x)/(x^2+1) on [-2,2]

Homework Statement Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.99 m away. If the first-order maxima are separated by 1.36 m on the screen, what is the distance between the two second-order maxima? Homework Equations I think these...

Let F=z_1\cos\theta_1\cos\theta_2+z_2(e^{i\alpha_1}\sin\theta_1\cos\theta_2+e^{i\alpha_2}\cos\theta_1\sin\theta_2)+z_3e^{i(\alpha_1+\alpha_2)}\sin\theta_1\sin\theta_2 where 0\le\alpha_i\le\pi,~0\le\theta_i\le\pi/2 and z_i are some fixed complex numbers. Then...

playing around with ctensor & the Schwarzschild metric in Maxima what is the difference between interior and exterior Schwarzschild metrics? also when with the exterior Schwarzschild metric the scalar curvature is zero - this cannot be right, can it?

question a rectangular plot of land requires fencing on all 4 sides. two opposite sides will use heavy duty fencing at £6/metre, whilst the other tow sides will use standard fencing at £3/metre. if the farmer buying the fencing has £5000 to spend, what is the maximum area he can enclose...

Hey everyone, I'm new to using the Maxima software and I'm having some trouble. When I enter the following formula to be evaluated: diff(1-exp^(-t/R*C),t); I get the following output: \frac{log\left( exp\right) \,C}{{exp}^{\frac{t\,C}{R}}\,R} This doesn't look right, even if I...

Homework Statement Please look at the attached picture In that I had to draw the line of maxima and minima Homework Equations line of maxima has greatest gradient line of minima has smallest gradient The Attempt at a Solution which line should be the maxima? the line with the...

Hi all, In my Calculus III course, we are using Stewart's book, so as you might know there is not much rigor in there. Likewise, when it came to the section on Maximum and Minimum values of a function with two variables z=f(x,y), they ommited a lot of stuff. Hence, i tried to use...

Homework Statement In a double slit experiment, the wavelength is 740nm, the slit separation is 0.140mm, and the screen is 48.0cm away from the slits. What is the linear distance between adjacent maxima on the screen? Please check my answer. Homework Equations dy/L = m*wavelength...

Homework Statement a)Yellow light Lambda= 589nm falls on a double slit. The distance between two slits is d=0.5 mm the width of each slit is a=100 micrometer. A screen showing the interference pattern is located 4 m behind the slits. Homework Equations What is the distance between...

Homework Statement Ramon has a coherent light source with wavelength 554 nm. He wishes to send light through a double slit with slit separation of 1.5 mm to a screen 90 cm away. What is the minimum width of the screen if Ramon wants to display five interference maxima? Homework...

Homework Statement Let f be continuous and positive on [a,b] and let M denote its maximum value. Prove: M = \lim_{n \rightarrow \infty} \sqrt[n]{\int_a^b (f(x))^n dx} Homework Equations The Attempt at a Solution Writing out the integral as a limit of Riemann sums, we have...

A rectangle is to be inscribed in a right triangle having sides 6 inches, 8 inches, and 10 inches. Determine the dimensions of the rectangle with greatest area. I recently tried doing it and the answer was found by finding the slope and then using the first and second derivatives of the area...

Are there any analytical techniques to do this besides the Derivative Test?

How will I find minima,maxima or both of one function (if they exist)? For example: f(x)=x^2-3x+2; f(x)=x^2-2x-x+2; f(x)=x(x-2)-(x-2); f(x)=(x-2)(x-1) x1,2=1,2 Those are the zeroes of the function. But how will I find the critical points (minima,maxima) of the function if x...

Homework Statement a) Light of wavelength 651 nm illuminates a grating with 3,424 slits per cm. If the screen is 1.08 m away, what is the spacing between the interference maxima? b) A laser cavity of length 0.2400 m, has reflecting mirrors at each end. What is the frequency, in GHz, of the...

Homework Statement Consider a crystal with planar spacing 3.2 A0. What order of magnitude of energies would one need for (a) electrons, (b) helium nuclei (mass = 4*proton mass) to observe up to three interference maxima? Homework Equations 2d.sinx = n.lambda (I) lambda = h / p...

Homework Statement I remember doing something very similar to this in pre-calc, but I don't know where to get started. A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cit out of each corner, and then the ends and sides will...

Homework Statement For a monopolist's product, the demand equation is: p = 42 - 4q and the average-cost function is c = 2 + (80/q) Find the profit-maximizing price. Homework Equations When i started to solve the problem, i deduced...

Does the distance between the maxima increase/decrease or stay the same when the slit separation is increased? when the slit width is increased? what about if it was minima? thanks for any help to understand how this works.

I hate to make another topic so soon, but I'd like to get some opinions on this question... Homework Statement A two slit electron difraction experiment is done with slits of unequal widths. When only slit 1 is open, the number of electrons reaching the screen per second is 25 times the...

do you know about any maxima tutorials other than those provided in their help section?

Homework Statement Problem goes like this: For a monopolist's product, the demand equation is: p=156-2q _ and the average-cost is c(ave)=120+112/q Homework Equations We need to find the total cost function in terms of c= The Attempt at a Solution...

Homework Statement A hypothetical star S has a planet P that moves in an elliptical orbit with period T . The minimum distance of P from S is d and the maximum distance is 1.7d. (i) find the maxima and minima of the magnitude of the acceleration of P, in terms of d and T . Homework...

Homework Statement A Michelson interferometer uses light from a sodium lamp. Sodium atoms emit light having wavelengths 589.0 nm and 589.6 nm. The interferometer is intially set up with both arms of equal length (L1=L2) producing a bright spot at the center of the interference pattern. How...

I have a function that is not giving me critical points for where their appears to be a maximum. from plot their seems to be a cp at approximately x=y=5 However, these are the cp's: cpx = -0.2618 -1.3090 1.8326 2.8798 -2.8798 -1.8326 1.3090 0.2618cpy = -0.2618...

How would we find the maximum surface area of a cylinder inscribed in a sphere of radius R. This problem is given in my textbook . I know concept of maxima and minima will be apllicable here but i can,t start and make the expression of surface area in a suitable manner. Anybody having answers

Red light with wavelength 713 nm pass through a double split with "split distance" 0.120 mm. The interference pattern gets observed on a screen that is 2.75 m from the double split. Find the distance between the two third order maxima we seeing on the screen. (My english is really awkward)