Differentials Definition and 236 Threads

Homework Statement First write f(x,y) = x^2 + xy + y^2 in terms of powers of (x+1) and (y-1) Then write the taylor's formula for f(x,y) a = (1,4) and p=3 Homework Equations We write taylor's formula as: f(x) = f(a) + sum[(1/k!)*D^(k)f(a;h)] + (1/p!)D^(p)f(c;h) where sum is from k=1 to p-1 and...

I don't get why we need to use differentials and why they are the way they are. For example: dy=f'(x)dx vs. the derivative \frac{dy}{dx}=f'(x) Why are they equivalent? Why are integrals written in the differential form? I don't get the purpose of it. (other than to be used as an...

In applied subjects, the differential is often treated as i.e C'(x) approximately equals C(x+1)-C(x) 1 is used instead of h as h->0 because we are talking about discrete units such as items or people. They argue it works because x>>1. i.e considering lots of items, x. However what is rigorous...

First off i'd like to say Hi to the forums, hehe. I didn't really see a new member area but I suppose this will do. Right now I'm kind of struggling with these two problems that I recently took a quiz on and didn't do so well. I've been trying to figure out how to work them out but i just don't...

Homework Statement the problem asks: Find \deltaf/\deltax and \deltaf/\deltay at x=1 and y=2 if z=f(x,y) is defined implicitly by 2x^{}2y/z + 3z/xy - xy\sqrt{}z = 3. Note that (1,2,4) is a point on the surface. Homework Equations Im not really sure how to approach this one. The...

Homework Statement the problem asks: Find \deltaf/\delta/x and \deltaf/\deltay at x=1 and y=2 if z=f(x,y) is defined implicitly by 2x^{}2y/z + 3z/xy - xy\sqrt{}z = 3. Note that (1,2,4) is a point on the surface. Homework Equations Im not really sure how to approach this one. The...

Homework Statement One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30(degrees), with a possible error of +/- 1 degree. a) Use differentials to estimate the error in computing the length of the hypotenuse b) what is the percentage error...

So this is a somewhat random question as I'm asking it not because I've ever seen it as any sort of homework problem or the like, but more that I just can't seem to find a good explanation for it. Long ago I first learned about taking limits and, eventually, calculus. And of course in working...

Can someone give me an intuitive definition for differentials? My prof said to brush up on them because we'll be seeing them lots in thermo. I don't need all the theory because I'll be seeing them in november in calc. Right now I just have to work with them. Are they just infinitely small...

Hi everyone! I want to ask something about differentials. I often visit this forum and I saw people write that dx is something infinitesimal. Well but i read some books about differentials.Some of them define dx equals [delta x] and some of them seem not to consider dx as infinitesimal...

HELP! limit and differentials 1. i can't seem to figure this out... if the differential equation dy/dx= y-2y^2 has a solution curve y=f(x) contianing point (o, 0.25) then the limit as x approaches infinity of f(x) is a)no limit b. 0 c. 0.25 d. 0.5 e. 2 he...

Homework Statement Sorry, this may sound dumb, but How do I use differentials to estimate the amount of tin in a closed tin can with diameter 8 cm and height 12 cm if the tin is 0.04 cm thick? Homework Equations The volume of the can is V = pi*r^2h. So dV= 2*pi*rh*dr The Attempt at...

So the problem says "Taking ln10=2.30 estimate ln10.3 using differentials." The only thing I thought of doing was to set an integral from 1 to 10.3 with 1/x being the equation I integrate, but I'm not sure if that is right. Any help?

"Find the general solution to the differential equation by separating variables: 3tany - dy/dx(secx) = 0" This is what I set up: 3tany dx = secx dy 1/secx dx = 1/3tany dy cosx dx = 1/3tany dy [int] cosx dx = [int] 1/3tany dy sinx = (1/3)ln|sinx| I'm stuck as to what to do next...

I'm having trouble solving first order differential equations for euler's method. right now I'm trying to figure out: y' = x + y y(0) = 1 i have: dy/dx - y = x p(x)=-1 , q(x)=x u=e^(-x) y=e^x [integral](xe^-x)dx .. i don't think I'm doing this right, where am i going...

Alright I just did the following question, and was hoping I did it right: Use differentials(or, equivalently, a linear approximation) to estimate the given number) cos 31.5* (* meaning degrees) f(x) = cosx f(31.5*) = ? a is chosen to be the closest number to the number evaluating in...

Ok, I have having problems with the folloing: http://www.physics.uc.edu/~simpson/pics/Desktop-Images/0.jpg How exactly do I do this? I thought all I did, for example with the first du, was set up 2 integrals, one for the dx part, and one for the dy part. I then thought for (i) the dx integral...

I am completely lost on these differentials! Can anyone help me make sense of them? Especially this question in particular: cot(46(deg)) (Sorry, I don't know how to make that small little circle thing that denotes degree) I'm supposed to use the method of differentials to estimate...

If I have (A + dA)dZ = A dZ + dAdZ Can I drop the dAdZ? Likewise, with (dT + 1)dT = (dT)^2 + dT Can I drop the (dT)^2? Is there any basis for these actions? Are (dU)^3 and (dU)^2 equivalent?

Hello. Are the following integrals equivalent: Integral from 0 to 5 of dx / x and Integral from 0 to 5 of dx / (x + dx) What about Integral from 0 to 5 of dx / (x + 2dx + dx^2) ? If they are all equivalent, why? (I have an intuitive answer, but it has 0 mathematical...

I was just wondering about the dx and the end of an integral and evaluating integrals by substitution. When you evaluate integrals by substitution you can treat the dx as the differential of x. This seems to convenient lol. Some one must ahve known that the dx in an integral was the...

Hi, I'm trying to take differentials of the following equation (p + \frac{a}{{V^2 }})(V - b) = C in order to find the partial derivative \frac{{\partial p}}{{\partial V}} I know there's an easier way to do it but I have to take differentials. I'm just not sure how to deal with the...

1. The profit function for a compnay is P(x)=-390+24x+5x^2-(1/3)x^3, where x represents the demand for the product(doghouse). Find the approximate change in profit for a 1-unit change in demand when the demand is at a level of 1000 doghouses. Use the differential. -my answer that i got is...

Please for the love of god help me. I have a fundamental misunderstanding of differentials and Leibniz notation. I'm confused as to even where I should begin. Please allow me to start off my explanation by showing how my book introduces u-substition: I have highlighted in red the parts I am...

How Does One Find The Differentials Of Power Functions. Examples Like A[x]^b[x]^c[x]^d[x]... Where Those Are Functions Of X? In Cases Where These Functions Are Power Towers Of Another Variable,what Happens?

I am trying to understand some effects of pressure differences and air density particularly as it relates to the good ole american made V-8. One of my questions: What is the "speed" of air when a pressure differential is equalized? Assume I have a cube that is exactly one cubic foot in...

If anyone could check this answer for me, it would be greatly appreciated. Find the equations relating the differentials on the curve 9y^2= x^3 +3x^2 at the points (1,\frac{2}{3}), (-2,\frac{2}{3}), (-3,0) Here's what I got: y'= \frac {x^2+2x}{6y} m @ (1,\frac{2}{3})= \frac...

What is the difference between an exact and and inexact differential? These were introduced in my physics 2 book with the first law of thermodynamics represented by differentials, dEint= dQ + dW Then, it has a note that says "Note that dQ and dW are not true differential quantities...

Hi, I've seen a couple of proofs for the chain rule, and I know this probably sounds stupid, but I'm wondering why it can't be proved as follows: given the real valued functions y=f(u), u=g(x) since dy, du, dx, are all real valued functions as well can't you just state...

Four positive numbers, each less than 50, are rounded to the first decimal place and then multiplied together. Use differentials to estimate the maximum possible error in the computed product that might result from the rounding. I took f(w,x,y,z) = wxzy and then you set df=xzy(dw)+wzy(dx) etc...

A hemispherical dome with radius 48 feet will be given a coat of paint 0.07 inches thick. Use differentials to estimate the number of gallons of paint that will be needed to paint the dome. Here's what I did: f(x+h) = f '(x)h + f(x) and v=4/3pi*r^3; r=48ft. volume of the dome...

Hi, I tried readin up on HSW and another resource about how differentials in automobiles work... and i am pretty confused. http://web.mit.edu/2.972/www/reports/differential/differential.html at that site i found good diagrams of it. I understand why the "planet and sun" gears arent...

I've posted something like this before, but this one questions usage rather than reliability. If f(x) = x^2, and I want to find the change between x at 10 and 11. I could just fill in values 11^2 - 10^2 = 21 Or I could make a differential dy = 2x dx dy = 2(10)(1) dy = 20 Just...

One application of derivatives from first year calculus is something called differentials. The intent is to find the change of something based on the derivative of a function and some sort of varialbe like time or a distance or something. Let's say you have this formula: y = x^2 now here is...

Greetings ! I'd appreciate some help in explaining, in general, what - extracting partial differentials of a function, means. I'm talking about a function like f(x,y,z). Does it mean that I need a single solution where I will have differentials for x,y,z of the func.? Example...

I need help with these type of problems badly. Here's one I'm stuck on. The period of a simple pendulum with small oscillations is calculated from the forumula T=2*pi*sqrt(L/g) Where L is the length of the pendulum and g is the acceleration of gravity. If the values of L and g have...