Differential calculus Definition and 77 Threads

Homework Statement The equation that has to be solved: y'' - y' - 2y = 2e^(-t) The problem I am having is that I don't understand why they equatate that part with the derivatives of the u parameters to 0. (see image) Here they first find the characteristic equation and write down...

Homework Statement A liquid is being filtrated by a filter with a cone form. The filtring tax is 2cm^3/min. The cone has 16cm height, 4 cm radius. The volume V is given by pi*r^2*y/2 where y is the height, r the radius. Discover a formula that relates the tax of variation of the liquid...

1. Prerequisites Before you study calculus, it is important that you have a mastery of the concepts that come before it. I found calculus difficult to master (I basically had to take Differential and Integral Calculus three times in a row!), and I think many students also find it challenging -...

Homework Statement Here's the link (I scanned my homework), since it's hard to type the entire question on here, considering the mathematics-related symbols. I just want to make sure you all understand what I am asking. http://i1056.photobucket.com/albums/...ash5dash55.png...

Homework Statement Need help with all of question 8 , any help would be appreciated thanks :D Homework Equations The Attempt at a Solution

Homework Statement Use partial differential calculus to show that if 3 quantities p, V, T are related to each other by some unknown but smooth (which means all derivatives are well defined) equation of state f (P, V, T ) = 0. Then the partial derivatives must satisfy the relation∂p/∂T = - (∂V...

Homework Statement I don't understand how this can be written like this: \frac{1}{(2x+1)^{1/2}}-\frac{1}{(2x+1)^{3/2}}=\frac{2x+1-1}{(2x+1)^{3/2}}=\frac{2x}{(2x+1)^{3/2}} What's the rule which makes this possible and explain please.

Homework Statement A ship moving at 8 mi per hour, Sails W for 2 hours, then turns N 30 E. A search light, placed at the starting point, follows the ship. Find how fast the light is rotating, (a) 3 hours after the start; (b) just after the turn. Homework Equations The Attempt at...

If I'm lucky enough to pass Precalculus this semester, I'll be taking Calculus 1 next semester. Just out of curiosity, what is the difference between differential and integral calculus? Also, how does the two of them relate to upper-level mathematics (e.i: Number Theory, Vector Calculus, Real...

HI guys, I just started university and I have no idea what is going on in my lectures. My lecturer doesn't explain anything well and he is also the bloke who takes my tutorials. Lose - lose situation! Anyways I am trying to learn this myself, but I am stumped on this question: Homework...

Homework Statement A projectile is fired straight upward with a velosict of 400m/s. From physics, its distance above the ground after t seconds is: s(t) = -16t^2 + 400t A Find the time and velocity at which the projectile hits the ground B Find the maximum altitude achieved by the...

Homework Statement Could anyone explain me how to solve this? Homework Equations f(x) = 1/x2 + 4x + 9 + x4 , f’”’(-2) = The Attempt at a Solution

Homework Statement Homework Equations The Attempt at a Solution a) (∂z/∂x)=-(∂f/∂x)*(∂z/∂f) i used that (AxB)=-(BxA) so i get (∂z/∂x)=-[-(∂z/∂f)(∂f/∂x)] =(∂z/∂x) is this correct if not can someone give me hints pls thanks

1. Hey all, For my calculus class we were giving the problem of solving for the optimization of a tin can using differential calculus. The problem was to find the minimum cost for any tin can of any height(as well as using the equation for the tin we had). The surface area of the cylinder was...

Homework Statement A spherical balloon is being inflated at the rate of 10 cu in/sec. Find the rate of change of the area when the balloon has a radius of 6 in. Homework Equations V = \frac {4}{3} \pi r^{3} and A = 4 \pi r^{2} The Attempt at a Solution \frac {dV}{dt} =...

Homework Statement the height of a certain hill is given by h(x,y)=10(2xy-3x^2-4y^2-18x+28y+12) wher y is the distance north and x is the distance east of south hadley a)Where is the top of the hill b) how high is the hill c) how steep is the hill at a point 1 mile north...

Homework Statement Find f'(x)= 16x - x-2 using first principles. Homework Equations x http://img153.imageshack.us/img153/8403/597137697c1f605c7a43d34qz4.png The Attempt at a Solution I used dy/dx and got 2x-3 + 16 but I get something different when I use the formula I attempted...

Ok I am doing 1st year maths at uni and I am finding the differential calculus course really hard, i was hoping people here could just help me with the ideas. firstly: Level curves - I am having trouble drawing out the level curves for functions of two variables. For f(x,y) = 2x + y - 5...

Any help is greatly appreciated! :smile: Homework Statement 1.Differentiate. http://www.webassign.net/www16/symImages/8/a/e5af282af9dd30006849e16c0b489b.gif 2.Find the derivative of the function. http://www.webassign.net/www16/symImages/c/8/fd38a158e810bff80a28202fbceb37.gif...

I need a refresher on my multivariable differential calculus. Does anyone know of something brief with lots of exercises (maybe something geared towards physicists)?

Just a question regarding Differential Calculus Application. Can anyone help me to solve this using differential calculus. Here it is: A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose the maximum area? thanks in advanced:D

English translation of Fichtenholz, "Integral & differential calculus" I've been recommended the book "Integral & differential calculus, vol I,II,III by G M Fichtenholz."" however I can only find a german version: "Differentialrechnung und Integralrechnung..." Would anyone know if...

This is biological application question, so the limit can't be negative infinity, which is what I would use as my answer for a regular question. The rate at which substance is eliminated from the body is proportional to the amount of substance present, and satisfies the differentail equation...

Frankly I don't know how to say this,I need some help In Differential Calculus. I'm talking about Banach space and those stuff,If it's possible if someone know a link to some online textbook,i need something that goes deep into every theorm of this branch of math. thx you already , you don't...

You are given the following information about the function f(x): i) There is an x-value x* approximately equal to 0.8 such that f(x*)=0 ii) f(0.7) = C is negative iii) m1 < f'(x) < m2 for 0.7 < x < 0.9 where m1 and m2 are positive constants Apple the Mean Value Theorem to f(x) on the...

Please help. For the function 1/(1-x) the Taylor polynomial of degree 3 about x=0 is: p(x) = 1 + x + x^2 + x^3 a. Find an upper bound on l R(x) l if x = 0.5 b. Write down the first three non-zero terms of the Taylor series for g(x) = 1/(4-x^2) Is there an easier way to do b other...

hey i need help with 2 differential calculus problems, i missed the lecture so i am clueless as how to how to solve this. i don't really want the answer, id rather someone show me the methods anywhere, here goes: 2) A street light is at the top of a 16ft tall pole. A woman 6th tall walks...