Calculus ii Definition and 106 Threads

Homework Statement Determine whether the following series converges absolutely, converges conditionally or diverges. Show your work in applying any tests used. sigma[k=1,inf] [(-1)^k*k/sqrt(k^4+2)] Homework Equations integral csc(x) dx = -ln|sec(x)+cot(x)| + C csc(x) = 1/sin(x) sec(x) =...

Homework Statement The sereis sigma[k=1,inf] [(-1)^k/k^p] converges conditionally for (a) p<1 (b) 0<p<=1 (c) p>1 (d) p=0 (e) None of the above Homework Equations The Attempt at a Solution The answer key said that (b) was the correct answer and I'm having trouble...

Homework Statement Which of the following functions are soltuions of the differntial equation y''+y=sin(x)? a) y=cos(x) b) y=sin(x) c) y=1/2*xcos(x) d) y=1/2*x*sin(x) Homework Equations The Attempt at a Solution I'm kind of lost on how to solve this problem. I don't think...

Homework Statement Find the power series for f(x) using the definition of taylor series expansion about a=9. f(x)=1/sqrt(x) Homework Equations The Attempt at a Solution Find the power series for f(x) using the definition of taylor series expansion about a=9. f(x)=1/sqrt(x) f(x) =...

Homework Statement Find the radius of convergence and the interval of convergence of the series sigma[n=1,inf] ((3x-2)^n/(n^2*3^n)) Homework Equations The Attempt at a Solution sigma[n=1,inf] ((3x-2)^n/(n^2*3^n)) I applied the Root Test p=lim n->inf |(3x-2)^n/(n^2*3^n)|^(1/n) = lim n->inf...

New Question (Changed Old one) - Taylor Polynomial - Upper Bound for Absolute Error Homework Statement (a) Find the 3-rd degree Taylor polynomial of sin(pix) centered at x=1. (b) Use (a) to approximate sin(1.1*pi) (c) Use the remainder term to find an upper bound for the absolute error in...

Homework Statement Determine if the series inf Sigma n/(2n+1) n=1 converges Homework Equations The Attempt at a Solution When i did this I originally I thought I would just apply the divergence test lim n/(2n+1) =/= 0 n->inf there fore I thought by the...

Hi, I was wondering if it was really necessary to evaluate improper integrals with limits? Could anyone really say I was wrong if I did something like find the area bounded by the region y=1/x^2, x=2, and the x-axis integral[1,inf] dx/x^2 = (-1/x)|[2,inf] = (-0)-(-1/2)=1/2 Like I don't...

Homework Statement Hi, I'm really struggling with trying to come up with the error bound when doing taylor series problems Use the reaminder term to estimate the absolute error in approximating the following quantitites with the nth-order Taylor Polynomial cnetered at 0. Estimates are...

Hi, If I'm given something like this for a problem, Approximate the given quantities using Taylor polynomials with n=3 sqrt(101) how do I know what I should set f(x) equal to? I could set it to many different things, sqrt(x), sqrt(x+100), sqrt(x+50). My answer would be very different...

Homework Statement Hi, I'm trying to solve the problem in the attachment. I was asked to evaluate the left hand side equation of the equal sign. I was unsure how to go about evaluating it so I consulted my solutions manual to look up the first step. The right hand side equation of the...

Homework Statement Find the arc length of the following curves on the given interval by integrating with respect to x y=x^4/4+ 1/(8x^2); [1,2] Homework Equations Let f have a continuous first derivative on the interval [a,b]. The length of the curve from (a,f(a)) to (b,f(b)) is...

Homework Statement Hi, I'm trying to solve this problem and guess I'm doing something wrong. Evaluate Integral tan(x)^5*sec(x)^4 dx Homework Equations integral tan(x) dx = ln(|sec(x)|) integral tan(x)^n dx = tan(x)^(n-1)/(n-1) - integral tan(x)^(n-1) dx tan(x)^2+1=sec(x)^2 The Attempt at...

Homework Statement Evaluate integral dx/(x^4-10x^2+9) Homework Equations The Attempt at a Solution Ok so I'm trying to solve this problem for my calculus II course as a homework problem and am lost. The first attachment you'll see how I attempted to evaluate the integral by...

August 22nd is my first day of school, I'll be taking Calc II. I'd like to prepare now. It seems like Calculus I and II at any given school generally use the same textbook, my Calc I textbook was only covered about half-way in calc I. However, I'm transferring and it's no longer the same...

Homework Statement Evaluate integral sqrt(x^2-9)/x dx Homework Equations The Attempt at a Solution I get this for my answer sqrt(x^2-9)+3sin^(-1)(3/x)+c which is apparently wrong because when I take the derivative of it I don't get the integrand my work is a attachment in this post wolfram...

Homework Statement Evaluate integral dx/sqrt(1-2x^2) Homework Equations The Attempt at a Solution My Answer: -cos^(-1)(sqrt(2)x)/sqrt(2) + c See my work in attachment Wolfram Alpha Answer: (sin^(-1)(sqrt(2) x))/sqrt(2)+constant...

Homework Statement Evaluate integral dx/sqrt(x^2-49) Homework Equations The Attempt at a Solution SEE POST #4 BELOW WITH ATTACHMENT TO VIEW MY SOLUTION EASIER TO READ i was trying to use a csc(theta) substitution and I don't see how my logic and math below is flawed but apparently I'm...

Evaluate integral sqrt(9-x^2)/x dx I get to here -3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c I plugged in for theta because originally I had this -3 ln|csc(theta)+cot(theta)|+3cos(theta)+c and I set x equal to a expression x=3sin(theta) Hence i had to...

Homework Statement Evaluate integral csc(x)^4/cot(x)^2 dx Homework Equations The Attempt at a Solution Apparently I'm doing something wrong, what I'm not sure, thanks for any help My Answer: 2*tan(x) - (sec(x)^2*tan(x))/3 + c integral csc(x)^4/cot(x)^2 dx used fact that...

Homework Statement Evaluate integral sin^(-3/2)(x)cos^3(x) dx Homework Equations tan(x)=sin(x)/cos(x) sin^2(x)+cos^2(x)=1 sin^2(x)=(1-cos(x))/2 cos^2(x)=(1+cos(2x))/2 integral cos(x)dx = sin(x) + c integral sin(x)dx = -cos(x) + c d/dx sin(x) = cos(x) d/dx cos(x) = -sin(x) a^m/a^n=a^(m-n)...

Homework Statement Evaluate integral( sin^3(x) cos^5(x) ) dxHomework Equations sin^2(x) + cos^2(x) = 1 integral x^n dx = x^(n+1)/(n+1) + c d/dx cos(x) = -sin(x) a^n*a^m=a^(n+m) The Attempt at a Solution I got -cos^6(x)/6+cos^8(x)/8+c Apparently I did something wrong SEE ATTACHMENT Thank...

Homework Statement Apparently I'm doing something wrong. I'm kind of lost as to what because I looked over my work several times. Homework Equations sin^2 x = ( 1 - cos 2x )/2 cos^2 x = ( 1 - sin 2x )/2 integral sin(x) dx = -cos(x) integral cos(x) dx = sin(x) The Attempt at a...

So I've apparently been given an assignment on Cauchy functions (it says here on the title), but I have no idea what that means. Nevertheless, here's my attempt to solve this problem: Given (1): f(x)=\frac{k}{\pi}\times\frac{1}{k^{2}+(x-\beta)^{2}} and (2): \hat{\beta}_{k}=arg\ max_{\beta}...

Homework Statement I spoke to a few people and pretty much everyone but me seem to know what is going on with a few questions. This question was one of the ones I stared blankly for a few minutes and then wrote down an answer \int_{0}^{2} e^{x^2} d\theta The Attempt at a...

Homework Statement This is the third problem of a project for a Calculus II course. My issue is with graphing. Below is the problem, and below that my tutors explanation via e-mail to try and help me. I understand everything thus far, except for how I go about graphing. I am not strong in...

I barely passed Calculus II, I got 50 in the whole course after finals and I had 56 before finals. The class avg was around a high D but I can't remember exactly now but that's besides the point. Calculus II at my college was integral calculus with some application of integrals(volume, surface...

To make a potentially novella-length post very short, I'll skip the useless back story and say only that I had perhaps the most haphazard and unsatisfactory introduction to Calculus I one can imagine. I completed most of the course in about four weeks, and three-quarters of my work remains...

1. Find the area of the surface generated by revolving y = (sqrt)(2x-x^2), x = [0,1] a. About the x axis b. About the y-axis This problem is from the section about surface area revolving around an axis. I actually did the problem but I am not sure on my answer. For around the...

I worked out these two problems and got an answer but was not sure about the answer... If you could just check it and if it is not write tell me what I did wrong or give me a step by step, it would be greatly appreciated. 1. A tank is formed by revolving y = 3x^2, x = [0,2] around the...

when going into university and completing first year calculus, how much harder is the proceeding levels of calculus, as in, are the concepts and methods just as hard to understand, or is it the same as calculus I all over again as if you have never seen calculus before?

Homework Statement A smooth vector field F has divF(1,2,3) = 5. Estimate the flux of F out of a small sphere of radius 0.01 centered at the point (1,2,3). Homework Equations Cartesian Coordinate Definition of Divergence: If F= F1i + F2j +F3k, then divF=dF1/dx + dF2/dy + dF3/dz The...

This is my situation, last week I took the AP Calculus BC exam, I feel like I did really poorly and even if they are going to curve it, I think I am going to end up with a 3 or 4. Now in this summer, I going to take a Calculus III at a college who has granted me exemption from prerequisites...

So I just found out my grade for Calc I and I got a B-. I'm pretty disappointed in myself because I feel like I could've received at least a B+/A- if I wasn't so lazy. There were exams/quizzes that I seriously didn't study for at all besides a quick 10 minute glimpse in my notes. So I think...

Homework Statement F = 2i + 3j through a disk of radius 5 in the plane y = 2 oriented in the direction of increasing y. Calculate the flux of the vector field through the surface. Homework Equations The Attempt at a Solution I know that I need to calculate the area vector...

I'm double majoring in Physics and Mathematics at a small liberal arts school, and I am currently a freshman, with a 4.0 GPA so far. Right now I am taking Calculus II, and I am becoming quite frustrated. I definitely understand the material, and have little difficulty with homework or...

Okay so our calculus professor has given us an assignment to do a project involving calculus. He found out that I was a gymnast and liked physics so he said that my project should relate calculus, physics, and gymnastics. I'm having problems coming up with an idea in which I can actually...

Homework Statement \int \frac{ \tan x \sec^2 x }{ \tan^2 x + 6 \tan x + 8 } dx Homework Equations The Attempt at a Solution \int \frac{ \tan x \sec^2 x }{ \tan^2 x + 6 \tan x + 8 } dx Okay I let... u=tanx du=sec^2x Then I got \int \frac{ u }{ (u+4)(u+2) } du Then...

Hi, I'm taking Calculus II in the Spring and I'm wondering what you guys did to succeed in that class. I know it's different for each school, but in general, I've heard calc 2 was integration hell. Anyways, here are some topics that was listed in the Fall Calc 2 final review, what should I look...

I hear that calc II is the hardest course in the calculus sequence. I am not sure why this is, but it is something that I hear constantly. Why is it considered to be so difficult? Are there a lot of formulas or are there many different applications of formulas, ideas, and logic? Obviously people...

Thank you in advance for the help! Homework Statement Find the center of mass of a thin plate of constant density (delta) covering the given region. The region bounded by the parabola y= x - x2 and the line y= -x Homework Equations See attachment question 15 p1 The Attempt...

Homework Statement I have two relatively similar problems: 1.) Sigma n=1 to infinity ((ln n)^3 / n^2) 2.) Sigma n=1 to infinity (1 / sqrt(n) * (ln n)^4) I'm to prove their convergence or divergence using either the direct comparison test or the limit comparison test. I understand...

I was wondering what you should be familiar with before taking Calculus II. I just finished the Calc I summer class and was wondering if I should go on to Calc II this summer or just go over Calc I some more... I mean I can solve all of the problems that were presented but we hardly had any...

Hey... This really sucks. I am in Calculus 2 and I have had 3 in-class exams, all 3 were A's. This last exam is take-home and it is entirely Maclaurin and Taylor series.. The only thing in the class to go over my head. Please help me out with these problems! Homework Statement Use...

I'm very unsure on how to do this equation... Someone PLEASE HELP! \intx^{3}\sqrt{}x^{2}+9 i do know that if you... let x = 3sec \vartheta dx = 3 sec \vartheta tan \vartheta du

Do you think that taking Calculus II and Linear Algebra in the same semester is too much? Or should I be fine? How hard is Linear Algebra? EDIT: I can't take them the same semester I just found out, do you think it is wise to take LA in a short semester over the summer, like 4 weeks?

Homework Statement Evaluate the following definite integrals using the Fundamental Theorem of Calculus: 1. 1 \int 4 ( (5x2+7x+5)dx ) 2. -5pi/6 \int 4pi/6 (−6sinx+7cosx) dx ) 3. 2 \int 4 ( (e^-4x)/((e^(-4x))+7) dx ) If it's unclear, the number on the...

I'm taking calc 2 right now and I want to start planning what classes in going to take next semester. I'm basically retaking the class for college credit, so I'm fairly certain I am going to get a B+/A-. Some people are telling me to take vector calculus while the other half are saying...

Yes, that's right, I said it. Most of the grad students, professionals, and upperclassmen are probably laughing at my title, either because they breezed through the course, or because they too, remember being a first semester freshman in engineering, and hearing such horrible things about...

"Work" (Calculus II) This is a problem from the chapter called "Work": A water tank in the form of an inverted right-circular cone is 29 ft across the top and 15 ft deep. If the surface of the water is 5 ft. below the top tank, find the work done in pumping the water to the top of the tank...