Calculus Definition and 1000 Threads

Homework Statement The problem (Spivak's Calculus, chapter 6, problem 17): "Let ##f## be a function with the property that every point of discontinuity is a removable discontinuity. This means that ##\underset {y \rightarrow x} {\lim} {f(y)}## exists for all ##x##, but ##f## may be...

Homework Statement I have to find length of the curve: y2 = (x-1)3 from (1,0) to (2,1) Homework Equations s = ∫ √(1 + (f '(x) )2 ) dx where we have integral from a to b The Attempt at a Solution I'm bit confused: I'm thinking of writing function regarding x, f(x)...

Homework Statement Hi everyone, I'm currently making my way through Spivak's calculus and got stuck in question 41 of chapter 5. It's important to note that at this point, the book has only reached the subject of limits (haven't reached continuous functions, derivatives, integrals, series...

I've been researching for the calculus behind geodesic domes, and specifically calculus related to parametric surfaces. I've found http://teachers.yale.edu/curriculum/viewer/new_haven_06.04.05_u#f, but unfortunately, it comes short of providing me the most needed information, and so far I...

Homework Statement I'm currently working through Spivak independently and have reached the problems at the end of ch. 1. The problem is: Prove that if 0 < a < b , then a < \sqrt{ab} < \frac{a+b}{2} < b Homework Equations Spivak's properties P1 - P12 The Attempt at a Solution I was...

A total derivative dU = (dU/dx)dx + (dU/dy)dy + (dU/dz)dz. I am unsure of how to use latex in the text boxes; so the terms in parenthesis should describe partial differentiations. My question is, where does this equation comes from?

Hi there all, I'm currently taking a course in Multivariable Calculus at my University and would appreciate any recommendations for a textbook to supplement the lectures with. Thus far the relevant material we've covered in a Single Variable course at around the level of Spivak and some Linear...

I tried my best but the result doesn't match the effort I've put in. First when I know my result I freaked out and questioned my competent. Am I mathematically-inept? Am I cut out for a Physics Phd? End up with ~70% on this course and I'm taking Calc 2 this December. I need to...

If I have a limit of a series then how can I convert it into integral. I know to convert a sum into an integral there must be Δx multiplied to each term and this must go zero. Can you please explain me the conversion of limit of series (normal series with no Δx) into an integral. Thank you.

I am currently a junior in high school and recently, my guidance counselor has been asking me a lot of questions about what I want to major in. Within the last 6-8 months, I have been leaning heavily towards a math major. That was until I started my calc class this year... I'm in AP Calc BC...

I'm struggling with the math used in my college's calc-based honors physics class, even though I've taken calculus 1. ---What are some good books/resources to learn the math used in introductory physics?--- Preferably, it'd be nice if the math was taught using examples in physics. Having that...

I don't understand a good portion of the non-algebraic math behind much of the physics in my first semester college class. I understand everything with algebra, and can solve all problems, but I don't understand the relationships with vector cross/dot products, calculus derivations, DE, etc...

I've been working on this one for a little bit, and I know I really just need to use the chain rule to solve it, but I can't seem to figure out how to set it up properly. Probably a dumb question, but I could really use some help on this!

Homework Statement Hello, a bowl is created when rotating the function f(x) = \begin{cases} 0, & 0 \leq x \lt 6 \\ (12/\pi)arcsin(x-6), & 6\leq x \leq 7 \end{cases} around the y-axis. Find the height (h) and the volume (V) of the bowl.Homework EquationsThe Attempt at a Solution So, I graphed...

Homework Statement Hello, I need some feedback on whether this reasons is correct. consider the series Examine the series for absolute convergence. Homework EquationsThe Attempt at a Solution How I have solved this, using the limit comparison test: we have: introducing we have that...

Homework Statement Hello, I´ve added an image where the task is shown. I am wondering about the integral bounds here. When doing the substitution, shouldn't the bounds be inf and 0? When using that u = ln x, i.e. u(0) =inf, u(1) = 0. Homework EquationsThe Attempt at a Solution

Homework Statement Find the sum of the series Homework EquationsThe Attempt at a Solution Not sure exactly where to start. If I move 3 outside the sum I'm left with 3*sigma(1/n*4^n), which I can rewrite to 3*sigma((1/n)*(1/4)^n), which party looks like a geometric series..Any tips?

Homework Statement Hello, I need to find an expression for the sum of the given power series The Attempt at a Solution I think that one has to use a known Maclaurin series, for example the series of e^x. I know that I can rewrite , which makes the expression even more similar to the...

Afternoon, I have been working on this problem for awhile now but have been stuck on a certain point, and once I set everything equal to each other I end up with the same thing for example: x=x, y=y, & z=z Find the minimum and maximum values of the function f(x,y,z)=3x+2y+4z subject to the...

Hi, I want to start learning physics as I have never studied it in my life but have now taken an interest towards it. I have quite literally zero knowledge on physics, so assume I haven’t taken middle school or high school courses on physics, as I haven’t. I’m 17 currently, but that shouldn’t...

I have been stumped on this problem and I am probably overthinking it as usual. The problem deals with the Lagrange Multipliers: Use Lagrange multipliers to find the point (a,b) on the graph of y=e^(9x), where the value (a,b) is as small as possible. I have found the gradient for both when...

Homework Statement Find the points on the surface xy^2z^3=2 that are closest to the origin Homework EquationsThe Attempt at a Solution x,y,z=/= 0, as when x,y,z = 0 it is untrue. Right?? Otherwise, I am very unsure as to how to approach this problem. Should I be taking partial derivatives to...

Homework Statement The question is to solve the inexact equation by turning it into exact.the equation is ##( x + y + 4 ) d x + ( - x + y + 6 ) d y = 0## Where "x" and "y" are variable. 2. Homework Equations [/B] 1.(x+y+4)=m and (-x+y+6)=n 2.Integrating Factor =##\frac { 1 } { x ^ { 2 } + y...

Greg Bernhardt submitted a new blog post A Numerical Insight for the Fundamental Theorem of Calculus Continue reading the Original Blog Post.

How do I know where to put the axes for the equation 4x^2 - 9y^2 = z when graphing in 3d?

Homework Statement Suppose light is prepared in a coherent superposition of linear horizontal polarization and linear vertical polarization. What is the resulting polarization according to Jones calculus if it passes through: a linear polarizer at a 45-degree angle (0 degrees would be...

Homework Statement Let D be the triangle with vertices (0,0), (1,0) and (0,1). Evaluate: ∫∫exp((y-x)/(y+x))dxdy for D by making the substitutions u=y-x and v=y+x Homework EquationsThe Attempt at a Solution So first I found an equation for y and x respectively: y=(u+v)/2 and x=(v-u)/2 Then...

The question goes like: find the SA of the portion S of the cone z^2 =x^2 +y^2 where z>=0 contained within the cylinder y^2+z^2<=49 this is my attempt using the formula for SA, I could switch to parametric eqns, but even then I'd have hard time setting up limits of integration.

Homework Statement Given the graph of f(x) shown below, find the value of the integral. Photo attached. Homework Equations [/B] ∫23 5x·f(x2)dx The Attempt at a Solution [/B] I tried integration by parts to simplify the problem, but finding the integral of the composite function (f(x2))...

I have the first and second orders that I use in a magnetic simulator, but i need the thirth also to do also with magnetic cylinders accordingly paper: Do anybody have it in any code? I should pass to C++

Homework Statement The equation 4x = (1/3)*cos(3x) has a solution on the interval [0,1]. Find an approximative solution by replacing the right hand side with a Taylor polynomial of degree 2 around 0. Homework EquationsThe Attempt at a Solution So as I understand the task we should find a...

The original problem for anyone that can read Chinese: https://zerojudge.tw/ShowProblem?problemid=b221 The problem defines a convex polygon with multiple points located in the first quadrant and the required task is to find a linear function y = ax that can spilt the polygon into two parts each...

Okay, I never took calculus 3 so I don't know how to write/solve an integral for a power I made up. I want to flesh out my game world with math because it's cool and I can. Like Chester wrote some of the physics for the Bizarro universe. Applying physics and math to a fictitious universe is...

Hi, I have decided I like to learn some physics as I know absolutely zero physics and also including chemistry or biology, and I’d like to learn a bit of all 3, to the high school level perhaps. It seems that from, what I’ve read if I want to learn chemistry, I’ll first have to know physics, and...

High school student here... Recently, I've found an interest in topology and am trying to figure out the correct path for self-studying. I am familiar with set theory and some concepts of abstract algebra but have not really studied any form of analysis, which from what I've read is a...

Homework Statement Use the integral test to show that the sum of the series gif.latex ##\sum_{n=1}^\infty \dfrac{1}{1+n^2}## is smaller than pi/2. Homework EquationsThe Attempt at a Solution I know that the series converges, and the integral converges to pi/4. As far as I´ve understood...

Hi guys! Here's a problem i was working on. I solved it by root test and got absolute value of x on the outside of the limit and the limit equaled zero. Is it wrong to multiply the outside absolute value by the zero I got from the limit? or is that okay? In general, when we are solving power...

<Moderator's note: Moved from a technical forum and thus no template.> I'm solving a problem using tuple relational calculus ( TRC) in DBMS. Problem Find the name of all the employees who work for XYZ Bank Corporation. Solution ( as given in my book) I don't understand why book is using...

Homework Statement Show that the equation arctan(x) = x^2 have at least one solution. Then argue why the equation only has one, positive solution r. Homework EquationsThe Attempt at a Solution I know how to prove that the equation has at least one solution (IVT), but I do not know how to show...

Homework Statement Let R be the area in the xy-plane in the 1st quadrant which is bounded by the curves y^2+x^2 = 5, y = 2x and x = 0. (y-axis). Let T be the volume of revolution that appears when R is rotated around the Y axis. Find the volume of T. Homework EquationsThe Attempt at a Solution...

hi, I'm a high-school student that is just beginning to learn calculus. in calculus we are learning how to apply integration and diffrentiaiton methods regarding kinematics. there is this certain phrase i do not really understand in our textbook: e.g."in the second second" how am i meant to...

Homework Statement a. Find a point at where these lines intersect b. Find the equation of a plane that contains the two lines. Homework Equations r[/B] = <1,3,0> + t<3,-3,2> r = <4,0,2> + s<-3,3,0> The Attempt at a Solution I correctly found the point of intersection to be...

Homework Statement a. Write down a Riemann sum for the integral ∫x3dx from 0 to 1. b. Given the following identity 13+23+33...+N3=(N(N+1)/2)2, show that the Riemann sums for ∫x3dx from 0 to 1 converge to 1/4. The Attempt at a Solution I believe I have gotten part a. I got ∑i^3/N^4 from i=0 to...

Homework Statement A container with height 4.5 is created by rotating the curve y = 0.5x^2 0 \leq x \leq 3 around x = -3 and putting a plane bottom in the box. Find the volume V of the box. Homework EquationsThe Attempt at a Solution I want to solve this by using the shell method. I have...

Hi, my name is "Bob" I have a particular question about a specific book. Preface... It has been a while since I formally studied Physics. The type of Physics book I remember using last was I believe, Algebra-based. This was in high school. Based on my degree, I studied Algebra and Trigonometry...

the question: My attempt: The partial derivatives did not match so i simply tried to find f(x,y) I got the set of equations on the right but that's about it.

I have recently started studying multivariable calculus and I cannot quite visualise the concepts.Problem solving is not a problem but I want a true understanding of the concepts.Which book or online resources are great at developing visualisation in this course?

Homework Statement Find a > 0 so the integral int(exp(-ax)*cosx)dx from 0 to inf get as high value as possible. The Attempt at a Solution My way of solving this is to plot the integrand, i.e. exp(-ax)*cosx and check for different values of a. The larger a is, the smaller the area under the...

Hi there , well my questions is in the title but i have to say some things : I have multiples mathematiques and physics courses calc-based and so i want to review the basic . I already search around this forum and others and i find some books who looks popular here there are : - Pre-Calculus...

Homework Statement Find the smallest value of b so that the function f(x) = x^3 + 9x^2 + bx + 8 is invertible. Homework EquationsThe Attempt at a Solution I know that the function has to be only increasing/decreasing, and I think it is needed to find the derivative of the function. I do...