Basic calculus Definition and 37 Threads

Hi PF, stucked with this proof: Taylor's Formula The following theorem provides a formula for the error in a Taylor approximation ##f(x)\approx{P_{n} (x)}## similar to that provided for linear approximation (...) Taylor's Theorem If the ##(n+1)##st-order derivative, ##f^{(n+1)} (t)##, exists...

I want a book that isn't too wordy, explains things concisely, and covers single-variable and multi-variable calculus. I regret that I forgot so much of the stuff I learned in Calculus III and IV (especially the important theorems I learned but forgot in the latter), and now I want to review it...

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...

Hello everyone, Reading Landau and Lifshitz Course of Theoretical Physics Volume 1: Mechanics (page 3) I got suck in the following step (and I cite in italics): The change in S when q is replaced by q+δq is \int_{t_1}^{t_2} L(q+δq, \dot q +δ\dot q, t)dt - \int_{t_1}^{t_2} L(q, \dot q, t)dt...

Problem: How fast is the area of a rectangle changing if one side is I0 cm long and is increasing at a rate of 2 cm/s and the other side is 8 cm long and is decreasing at a rate of 3 cm/s?I have 2 approach and I want to know which is correct, why and what am I missing

Homework Statement I need to draw this function: however I don't get how? I have the solution but I don't understand how do I get that from the given function. Someone please try to explain? Thanks

Hi! First time poster, I'm about to enter first year calc and thought that I could get ahead of the curve by checking out some questions beforehand. This showed up on one of the university calculus exams but I couldn't figure out how to do it. I tried to finding a common denominator but then was...

So, I was doing a question on Laurent series. Part of it asked me to work out the pole of the function: $$ exp \bigg[\frac{1}{z-1}\bigg]$$ The answer is ##1## - since, we can write out a Maclaurin expansion: (1) $$ exp\bigg[\frac{1}{z-1}\bigg] = 1+\frac{1}{z-1}+\frac{1}{2!}\frac{1}{(z-1)^{2}}...

I am a beginer. I have read that any given signal whether it simple or complex one,can be represented as summation of orthogonal basis functions.Here, what the terms orthogonal and basis functions denote in case of signals? Can anyone explain concept with an example?Also,what are the physical...

Homework Statement Prove that sinx+cosx is not one-one in [0,π/2] Homework Equations None The Attempt at a Solution Let f(α)=f(β) Then sinα+cosα=sinβ+cosβ => √2sin(α+π/4)=√2sin(β+π/4) => α=β so it has to be one-one [/B]

Homework Statement A police car is parked 50 feet away from a wall. The police car siren spins at 30 revolutions per minute. What is the velocity the light moves through the wall when the beam forms angles of: a) α= 30°, b) α=60°, and c) α=70°? This is the diagram...

Hey guys, I'd appreciate some help for this problem set I'm working on currently The u-substitution for the first one is somewhat tricky. I ended up getting 1/40(u)^5/2 - 2 (u) ^3/2 +C, which I'm not too sure about. I took u from radical 3+2x^4. For the second question, I split the integral...

This is my first post, and I'm excited to be able to receive quality help from what seems to be a good place. I'll attempt to start using the proper format and make it easy for everyone to read, thank you for the help! This should be a simple problem, but I seem to have forgotten how to do it...

lim of (3^y-5^y)/(2^y-7^y) as y->0 Evaluate the above limit. Okay, so, I was flabbergasted at how challenging this problem is. I realized it was an indeterminate form [0/0]. I was trying to find a way to cancel y out of the numerator and denominator, in vain. I tried finding a pattern to...

Homework Statement See attached. Homework Equations The Attempt at a Solution I integrated the equation with respect to x to obtain ∫\frac{d}{dx}(xe^{-x}\frac{df}{dx})dx+∫ne^{-x}fdx= constant The first term on the left hand side goes to zero as x, df/dx are bounded at 0...

Could someone point me to the proof or reasoning behind the steps: 1) a = dv/dt 2) a dt = dv 3) ∫a dt = ∫dv I know this works, but I'm missing understanding in the math behind it, and I'm not sure what to type into google. Thank you very much

I will be taking calculus soon and want to know what yo expect from the course. please give as many details as possible. thank you

Hello everyone, I have an integral of the following form: log(\int_{r}^{\inf}\frac{P(r,f)}{P(f)}dr) Now, my question is that since the integral is wrt to r, can I bring P(f) outside. So: \frac{1}{P(f)}log(\int_{r}^{\inf}P(r,f)dr) Thanks, Luca

It's been a while since I've done calculus and now a simple derivative is stumping me. This is the issue: d(xf)/dx= ? This is just the product rule, so I think: x(df/dx) + f (dx/dx)= x (df/dx) + f But I'm afraid that I don't even understand my own notation anymore (how...

Homework Statement Basic Question. My book describes the rate of heat transfer per unit of system area as \dot{Q}=\int\dot{q}dA. The Attempt at a Solution I'm trying to solve for the flux. I've already discovered that the correct answer question is just the derivative of \dot{Q} with respect...

Hi, I am a biology major starting my freshman fall quarter in about two weeks. I have always struggled with math (mostly due to a lack of effort). However, over the summer, I have made huge strides in my progress as I have been working extremely hard to master algebra and pre-calculus in...

I always seem to find this place whenever I'm in need of homework help, so I finally decided to register (and hopefully post in the right area). My given problem is Here are three displacements, each in meters: d1 = 4.2i + 2.7j - 7.9k, d2 = -1.0i + 2.0j + 3.0k, and d3 = 4.0i + 3.0j +...

For my practical engineering degree in mechatronics, we only studied really basic calculus. How to take derivatives and intergals of simple functions. I'm curious, is "basic calculus", which is like 1/5 of calculus I I guess, all you really need for engineering? *We were told there won't be any...

Homework Statement If sinx(lnx)=0 over [0, 2pi] then x=_____ The Attempt at a Solution My attempt was to move sin over to the other side to get lnx= 0/sinx and then get lnx=0, making x=1. But is it incorrect to just move sinx over to the other side, because if i move lnx over to...

It's a basic calculus problem for some uni homework, but it's been a while and I'm rusty. More or less just looking for a check on my work Homework Statement Differentiate: v(t)= 6e^(-t).ln(t+5) The Attempt at a Solution Using the product rule: v'(t) = du/dt(6e^(-t)).ln(t+5)...

Homework Statement A water tank is in the shape of a half cylinder sitting on its side (not its top or its bottom). Let the radius be 10 ft and let the side-lenth on the floor be 30 feet. What should be the water height, measured from the floor up, so that the water tank is half full...

Okay, I am new to calculus so can you guys just explain something to me. What is exactly are you doing to a function when you differentiate or take the derivative of it? I thought that when you do that, you make an instantaneous solution to where something is at all times with respect to the...

Homework Statement Q) Derive the dereitvative of sinΘ using the definition of differentiation. I am in Calculus 3, and I used to know how to work this problem very well! :) I just don't remember lol - I just need a little help I guess! :) Homework Equations lim [f(x+h) -...

Homework Statement A point charge +q is located a distance d from one end of a uniformly charged rod. The rod has total charge +Q and length L. (The rod and the point charge are each held fixed in place.) What is the force on the point charge due to the rod...

Homework Statement Find the first and second derivatives of the function. Homework Equations The Attempt at a Solution This was an even problem, so I have done the work but not completely sure that my answers I got are correct. Here's what I got: Much appreciated, Bob

I have been going over some lecture notes and have some questions about some of the mathematics shown in these notes. They start off with the following equation: \delta F_x = \dot{m} \frac{dV_x}{ds} \delta s and then impose the limit as \delta s \rightarrow 0, and gets...

can someone please convince me that lim x->0 sqrt(x) = 0 Who of you say it doesn't exist?

It's been a while since I studied calculus and basically I have a review sheet for a course I'm taking, but not a graded assignment. So, I was hoping if anyone knew a resource to point me in the right direction with a couple of problems: \int_0^\theta x^a dx Where a is not an element...

Homework Statement Find the Arc Length Parameter along the curve from the point where t = 0 by evaluating the integral: s = ∫ |v(τ)| dτ from 0 to t Then find the length of the indicated portion of the curve. Homework Equations The vector I am using for this: r(t) = (etcos t)i + (etsin...

I am trying get started in physics and i want to get a physics book with $only basic calculus$. do anyone suggest anything?

http://www.karlscalculus.org/" It has sections on - Number Systems - Limits - Continuity - Derivatives - Applications of Derivatives - Exponentials and Logs - Trig Functions - More Tricks with Derivatives - Integrals - Methods of Integration - Applications of Integrals The...

Hi I have a basic question on calculus ...please can someone explain to me : Let f(x) = x^2 y + delta y = f ( x + delta x ) The book says that a small increase in x will cause a small increase in y. But if I put let's say 3 and 2 for x and dx y is 5^2 which is 25. But...