Calculus Definition and 1000 Threads

I wrote a Calc II midterm today. Things went quite well, except for one question. I left it blank, as I did not have sufficient knowledge to write anything that made any sense. The question was worth 10% of the exam mark. This question was about a part of a section we covered, but this part had...

Homework Statement For some reason it is not letting me add the image here, here is the link to the question: http://imgur.com/a/3DLWM The part I'm stuck on is the last part. Basically, the question is to obtain the following equation for the entropy of vaporisation using the Redlich-Kwong...

Just curious.

Homework Statement Suppose there is an object that is a distance ##r_0## from the center of a planet that is nearby (the object is outside the surface of the planet). Let ## r ## represent the distance from the object to the planet's center. Let ## t ## represent time. The object, which is...

hi guys i want a good book for self learning calculus and i found caculus by Swokowaki and olnick 6ed i bought it actualy for 1.5$ (used version) so i want to know is it a good book for self learning or there's better one? i actualy took couple courses in calculus ,algebra, geometry in collage...

Homework Statement Today i had a test on definite integrals which i failed. The test paper was given to us so we can practise at home and prepare better for the next one. This is the first problem which i need your help in solving:: Homework Equations 3. The Attempt at a Solution [/B] As no...

The Complete Idiot's Guide to Calculus INTRODUCTION I've never really been very good at math and when I found out I had to take a Calculus class I started to panic. Once I gathered myself I went to the local bookstore to see if I could get a book to read so i could get a heads start. We are...

Hey everyone, I'm a CS major, and haven't been using calculus 1 or 2 for over a year and a half now. I vaguely remember any of it other than basic concepts (what derivatives and integrals are, second derivative, inflection points, etc.). I am taking an Introduction to Probability and...

I have recently finished an extensive review of vector calculus. I need to connect the exhaustive techniques of Surface Integrals and line integrals to quite a few problems involving Maxwell's Equations before I really feel certain that I am on board with both the math and the physics. I feel...

Homework Statement Determine the FIRST maximum and minimum values of the underdamped oscillation: y=e^(-x/2)(4sin(3x)+3cos(3x)) cm Homework Equations 3. The Attempt at a Solution [/B] I firstly differentiated the above equation and got: (-e^(-x/2)(22sin(3x)-21cos(3x)))/2 I checked this and...

Homework Statement ##f(x) = \begin{cases} -\frac{1}{1+x^2}, & x \in (-\infty,1) \\ x, & x \in [1,5]\setminus {3} \\ 100, & x=3 \\ \log_{1/2} {(x-5)} , & x \in (5, +\infty) \end{cases}## For a given function determine the truth of the folowing statements and give a brief explanation: a) Function...

Homework Statement Suggest an integral that is reduced to a rational function integral when this substitution is used: ##a)## ##t=\sin x## ##b)## ##t=\sqrt[6] {x+5}## ##c## ##\sqrt{1-9x^2}=-1+xt## Homework Equations 3. The Attempt at a Solution [/B] I found this to be a very interesting...

Homework Statement I have a couple of series where I need to find out if they are convergent (absolute/conditional) or divergent. Σ(n3/3n Σk(2/3)k Σ√n/1+n2 Σ(-1)n+1*n/n^2+9 Homework Equations Comparison Test Ratio Test Alternating Series Test Divergence Test, etc The Attempt at a...

What would tou suggest as the best resource for learning integrals? I need preferably some practical books videos or youtube channels that deal with application and problems rather than theory. Any thoughts? Thanks

In the solution of this problem(121), dW = (kmgcosΦ + mgsinΦ) ds, where ds is the differential element along the curve. Now they have done kmg dscosΦ + mg ds(sinΦ) = kmgdx +mgdy. Makes sense intuitively, but I want to know how this is rigorous. What I'm thinking is, the curve is broken into N...

In the solution of this problem(121), dW = (kmgcosΦ + mgsinΦ) ds, where ds is the differential element along the curve. Now they have done kmg dscosΦ + mg ds(sinΦ) = kmgdx +mgdy. Makes sense intuitively, but I want to know how this is rigorous. What I'm thinking is, the curve is broken into N...

Homework Statement Find the equation of the tangent line to the curve ##\ xy^2 + \frac 2 y = 4## at the point (2,1). Answer says ##\ y-1 = -\frac 1 2(x-2)## And with implicit differentiation I should have gotten ##\frac {dy} {dx}= -\frac {y^2} {2xy-\frac {2} {y^2}}## Homework Equations ##\...

I have calculus textbook that is 352MB I want to split it into chapters the book is 1050 pages I used one the free online splitters to cut out a chapter earlier. but now I can't find it. there are MB limits so I'm over I thought the acrobat reader on the University pc would do it but the...

General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.

I read people saying that dy/dx is not a ratio because it is a limit or standard part of a ratio. $${dy\over dx} = \lim_{h \to 0} {f(x +h) - f(x) \over h}, \ \ \ {dy\over dx} = st\left( {f(x +h) - f(x) \over h}\right)$$ what I get is ##{f(x +h) - f(x) \over h}## is a ratio but putting a limit...

Homework Statement The function h is differentiable, and for all values of x, h(x)=h(2-x) Which of the following statements must be true? 1. Integral (from 0 to 2) h(x) dx >0 2. h'(1)=0 3.h'(0)=h'(2)=1 A. 1 only B.2 only C. 3 only D. 2 &3 only E. 1,2 &3 Homework Equations None that I am...

Say a particle cover y=t^2 distance. at t=1s total distance cover = 1m at t=2s total distance cover = 4m at t=3s total distance cover = 9m at t=4s total distance cover = 16m So the instantaneous speed at t=2s is 9 - 4 = 5m i.e 5m/s. To get the instantaneous speed at t=2s and...

Homework Statement Hi, I am not asking for solution for any problem as i already have the given solution for the problem. Instead, what i want clarify is what do they mean by the odd and even function and how do they get 0? Also, is there a need to change the order from dxdy to dydx?

Homework Statement Find the maximum and minimum value attained by f(x, y) = x2 + y2 - 2x over a triangular region R with vertices at (0, 0), (2, 0), and (0, 2) Homework Equations partial x = 0 and partial y = 0 at extrema The Attempt at a Solution partial x = 2x - 2 partial y = 2y 2x - 2 =...

Homework Statement Where are the following functions discontinuous? f(x) = (x+2)/√((x+2)x) Homework EquationsThe Attempt at a Solution f(x) = (x+2)/√((x+2)x) = (x+2)/x√(2x) multiply both denominator and numerator by √(2x) = (x√2+2√x)/(x(2x)) Can I leave it like this and state that x ≠ 0, or...

Sorry, I mistakenly reported my own post last time. But later I realized that these limits do work. So, I'm posting this again. I'm using these limits to check second-order differentiability: $$\lim_{h\rightarrow 0}\frac{f(x+2h)-2f(x+h)+f(x)}{h^2}$$ And, $$\lim_{h\rightarrow...

I am trying to come up with an analytical solution (even as a infinite series etc.) for the following diffusion-convection problem. A thin layer of gel (assumed rectangular) is in direct contact with a liquid layer (perfusate) flowing with velocity v in the x direction (left to right) just...

<Moved from a technical forum, therefore no template.> How is it coming (-1)^n(p+n-1)!/(p-1)! please help...!

Homework Statement Question: To solve the integral ##\int \frac{1}{\sqrt{x^2-4}} \,dx## on an interval ##I=(2,+\infty)##, can we use the substitution ##x=\operatorname {arcsint}##? Explain Homework Equations 3. The Attempt at a Solution [/B] This is my reasoning, the function ##\operatorname...

Γ(n) = ∫x→∞ tn-1 e-t dt?

d is sometimes used to represent an infinitesimal change in a quantity and sometimes a small amount of a quantity. E.g dx vs dM. dV could mean a small volume element and also an infinitesimal change in volume. How can it be used for two different things? My suspicion is that while converting...

I would like to start learning my calculus course before in school. Are here any textbooks or science reading books that would help me with the situation?

Let's talk about the function ##f(x)=x^n##. It's derivative of ##k^{th}## order can be expressed by the formula: $$\frac{d^k}{dx^k}=\frac{n!}{(n-k)!}x^{n-k}$$ Similarly, the ##k^{th}## integral (integral operator applied ##k## times) can be expressed as: $$\frac{n!}{(n+k)!}x^{n+k}$$ According...

This question has a little bit of physics in it, but it's mostly maths. If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz. However, in this case, I had to calculate the work done by the spring force as a function of y Over here, I...

If I have force, or any function f(z), I was told that I can assume it to be constant only in the interval dz. However, in this case, I had to calculate the work done by the spring force as a function of y Over here, I assumed the spring force, which is a function of its elongation x (F =...

I'm a bit torn on what the difference between analysis and calculus is, I read somewhere that calculus is pretty much analysis without proofs? Either way, I see a lot of people mention problems being on calculus 1 or 2 level. I have finished Analysis 1 and 2 and covered stuff like (series, ODE...

I understand the conditions for the existence of the inverse Laplace transforms are $$\lim_{s\to\infty}F(s) = 0$$ and $$ \lim_{s\to\infty}(sF(s))<\infty. $$ I am interested in finding the inverse Laplace transform of a piecewise defined function defined, such as $$F(s) =\begin{cases} 1-s...

This is mostly a procedural question regarding how to evaluate a Bromwich integral in a case that should be simple. I'm looking at determining the inverse Laplace transform of a simple exponential F(s)=exp(-as), a>0. It is known that in this case f(t) = delta(t-a). Using the Bromwich formula...

Consider the function: $$F(s) =\begin{cases} A \exp(-as) &\text{ if }0\le s\le s_c \text{ and}\\ B \exp(-bs) &\text{ if } s>s_c \end{cases}$$ The parameter s_c is chosen such that the function is continuous on [0,Inf). I'm trying to come up with a (unique, not piecewise) Maclaurin series...

So I decided to try deriving a general formula for fun. Being a high school student, the calculus got scary very fast. At this point, I'm just curious as to what the best approach to this might be. The approach I used was finding y as a function of x and then inputting it into the arc length...

Hi All, $$\int{\exp((x_2-x_1)^2+k_1x_1+k_2x_2)dx_1dx_2}$$ I can perform the integration of the integral above easily by changing the variable $$u=x_2+x_1\\ v=x_2-x_1$$ Of course first computing the Jacobian, and integrating over ##u## and ##v## I am wondering how you perform the change of...

Homework Statement Find the total tension acting on a rod rotating about its end with an angular velocity of w as a function of its length x(length) Homework Equations F = ma[/B] The Attempt at a Solution Let the function be T(x) where x is the length of the rod. Considering an interval...

Homework Statement limit (x -> 0 y -> 0) of xy/sin(x+y) Homework Equations None that come to mind but maybe Lopital's Rule The Attempt at a Solution I know that the limit does not exist but I am having trouble figuring out how to show that it does not using the line x=y gives x^2/sin(2x)...

Homework Statement [/B] Summarizing: two civilizations hate each other, one of the civilizations throws a curse at the second. The second civilization succumbs to chaos and has a change in Population each week of ΔP= -√P. That is: Pn = Pn-1-√Pn-1 Homework Equations [/B] Considering that the...

1. If x and y are arbitrary real numbers with x < y, prove that there is at least one real z satisfying x<z<y.2. I'll be using this theorem: T 1.32 Let h be a given positive number and let S be a set of real numbers. (a) If S has a supremum, then for some x in S we have x > sup S - h.The Attempt...

From Courant's Differential and Integral Calculus p.13, In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral. Proof: Let ##A=(0,0)...

Hello PF I have attached two screenshots from Goldstein's Classical Mechanics. Although I have done a course on multivariable calculus, I don't understand what is going on in this math part. Could you please provide some online resources or suggest a book so I can understand this sort of...

Hello. I am having a lot of trouble trying to solve/analyse this integral: $$\displaystyle \int_2^\infty \frac{x+y}{(y)(y^2-1)(\ln(x+y))} dy$$ I have tried everything with no result; it seems impossible for me to work with that natural logarithn. I have also tried to compute it, as it...

Hello! I have the equation FM = qvBsinθ . As the end result, I am trying to figure out what B I need to change θ even a little bit. To do that, I was planning to find the minimum B by differentiating B=(μe/4π)(qv x R / R3) in terms of R and setting it equal to zero. . I am assuming that this...

Homework Statement Find the externals of the functional $$\int\sqrt{x^2+y^2}\sqrt{1+y'^2}\,dx$$ Hint: use polar coordinates. Homework Equations ##x=r\cos\theta## ##y=r\sin\theta## The Attempt at a Solution Transforming the given functional where ##r=r(\theta)## yields...