Calculus 2 Definition and 117 Threads

Just finished taking my calculus 1 final now I'm ready to take calculus 2 in the fall. The question is how should I prepare for calculus 2? What are the important trig and calculus 1 sections I should study beforehand? Thanks.

I am in my first semester of university and currently taking Linear Algebra. I was planning on majoring in EECS but I lost interest in EE and engineering in general (except software) and gained a lot of interest in maths (especially statistics and financial mathematics) so I will double major in...

Homework Statement Find d2/dx2 0∫x (1∫sint√(1+u^4)du)dtHomework Equations The Attempt at a Solution Initially I treated this problem as the second derivative of a double integral and thus quickly found myself at the result cosx√1+sin4x, by the fundamental theorem of calculus. However I...

So...What's Calculus 2 like? So I just completed Calculus 1 with an A+ for the semester. What should I be expecting in Calculus 2 if the topics in Calc 1 were limits, differentiation, applications of differentiation, some integration, natural logs, logs, e, and hyperbolic functions?

Hello everybody!Could you tell me where I can find exercises with solutions of Calculus 2 online?Thanks! :rolleyes:

Homework Statement A tank containing 400 liters of water has 10 kg of salt solute (dissolved salt). Some brine containing 0.03kg/L of salt is then introduced at a rate of 2 L/min. The solution is constantly mixed and evacuated at a rate of 2L/min, such that the volume remains constant. If...

Hello users!,, What do you think about taking calculus 2 on summer? Im studying/teaching myself , and I want to know which topics should i focus to do very well in class.. Integration by parts?? Trig Sub? Thank you very much,, hope you ca help me.

Calculus 2 for summer?? Hello users!,, What do you think about taking calculus 2 on summer? Any of you have taken that course in summer? What can you say about it? Is it hard?? Also veryy important,, i got an A- in calc 1 I like math Im taking the course on july 11, it ends at...

Calculus 2- Water pump problem Homework Statement The lower half of a sphere with radius 2m is filled with water. Find the work needed to pump the water to a point 1m above the centre of the sphere. Homework Equations The Attempt at a Solution I know you have to cut the problem...

Alright, I have my final for Calc 2 on Monday. I am only stuck on two sections of problems because I am terrible at convergence and divergence/alternating series. I have questions for each one really. They are as follows: 4) a. Can I simply factor out the alternating series and apply a...

Calculus 2: Sequence Limits Question to the power n?? Homework Statement Find the limits (if it exists) to decide which sequences, whose nth term is given below. Homework Equations (\frac{3^{n}-4^{n}}{3n^{2}+4^{n}+7}) The Attempt at a Solution I've done a few of these but as Soon as the...

We learned integration, sequences/series + taylor series, and multi-variable calculus in 1 semester. I'm so overwhelmed for the final today.

Homework Statement Use substitution to show that for any continuous function f, $$\int_0^{\pi/2} f(\sin x)\,dx = \int_0^{\pi/2} f(\cos x)\,dx.$$ Homework Equations $$\cos(\pi/2-x)=\sin x$$ The Attempt at a Solution My confusion is that f is inside the integral, and I have no idea...

Uniform semi circle of radius R whose diameter is on the x axis. Since it is uniform and symmetric on the x axis, x = 0. For y, we have $$ y_{cm} = \frac{\int y\sigma dA}{\frac{\pi R^2}{2}} $$ In polar, $dA = rdrd\phi$. So the integral becomes $$ \int_0^{\pi}\int_0^R y^2\sin\phi drd\phi $$ How...

Homework Statement Not sure if this goes here or physics, but this is for my calculus 2 class so I decided here would be best. #22 Homework Equations W=∫Fdx The Attempt at a Solution I think the limits of integration are from 0 to 1 since the water is right under the spout, but...

I just finished taking Calculus 1 at a CC last semester. This coming semester, I will be taking Calculus 2, which will be my last semester of Calculus (woohoo!). I didn't take Precal seriously during junior year of high school (had an eating disorder that made me unable to concentrate and...

Let: 1) m be a constant 2) P ,K be one place operation symbols 3) F be two places operation symbol4) H,G be two places predicate symbols Let, the following assumptions:1) $\forall A\forall B [ H(A,m)\Longrightarrow G[P(A),B]\Longleftrightarrow G[K(B),A]\wedge H(B,m)]$2) $\forall A\forall B[...

Hi, you guys. I am going to take Calculus 2 next semester... And I would not say I am a math genius or anything... :/ So do you know of anything helpful to understand Calculus 2 very well? I want to study some over the break to have a head-start. Thank you! :)

Next semester I will be taking Calculus 2. I have used Courant and a little of Spivak for Calculus 1, and loved it! Extremely complete and challenging. Great books. So, this is exactly what I will need to know: Ordinary differential equations Families of equations, initial value...

My university's prerequisite is calculus 1 (which I've taken AP Calculus AB) to take Physics 1 (calculus based). My question is should I wait until I've completed calculus 2 to take physics 1? I've taken AP Physics B and did relatively well in it (although I don't remember everything perfectly..)

1) 1. y=x, y=sinx, x=-∏/4, x=∏/2 find the area between these limited curves. 2. ∫(upper function-(lower function) 3. ∫x-sinxdx(between x=-∏/4, x=0) + ∫sinx-xdx(between x=0,x=∏/2). Am I right? If it's okay,I don't have a problem in this integral. 2) 1. ∫sin(2x)/sin^2x(^=power)dx 2. I'm not...

I have some problems here with Series and Convergence... Here are the problems and my guesses at it. http://img822.imageshack.us/img822/9523/23341530.png It won't tell me which one is wrong, but it just says one/all is wrong. Any help is appreciated. Attempts at solving, I tried...

Homework Statement Find the volume: y=x, y=0, x=2, x=4; about x=1 Homework Equations Washer method V= ∏∫ (R)^(2)-(r)^(2) dy The Attempt at a Solution 0 to 4 is my a to b** ∏∫(from 0 to 4) of (1-4)^(2)-(1-y)^(2) dy ∏∫(from 0 to 4) of 9-(1-2y+y^(2)) dy ∏∫(from 0 to 4) of 8 +...

Homework Statement Find the slope of the line tangent to the polar curve at the given point. At the point where the curve intersects the origin, find the equation of the tangent line in polar coordinates. r = 6 sinθ; (-3 7∏/6) Homework Equations The Attempt at a Solution...

Sense e^x=Ʃ[k=0,∞] x^k/k! then ln(e^x) = ln(Ʃ[k=0,∞] x^k/k!) x = ln(Ʃ[k=0,∞] x^k/k!) is this true?

Determine how many terms of the convergent series must be summed to be sure that the remainder is less than 10^-4. Ʃ[n=1,∞] cos(k)/k^(3/2) I'm not sure how to solve this problem. I'm only aware of remainder formulas for the integral test and for alternating series. I'm not sure that this...

Determine if the following series converges or diverges: Ʃ[k=1,inf] ( k^2-1 )/( k^3+4 ) I don't see how to solve this problem the divergence test is inconclusive the ratio test is inconclusive the root test is inconclusive the integral test... not sure how to integrate this... the...

Homework Statement Determine if the following series converges or diverges. Ʃ[k=1,inf] tan(k)/(k^2+1) Homework Equations The Attempt at a Solution I have no idea how to solve this problem. Now that I think of it, I have never solved a single question about series were I'm...

This is a similar question that I have to the other one that I posted. Determine if the following series converges or diverges. sum[k=1,inf] 3/(k(k+3)) I applied the limit comparison test with 1/k^2 also k(k+3))=k^2+3k lim k->inf [ 3/(k^2+3k) ]/[ 1/k^2 ] = lim k->inf (3k^2/(k^2+3k)...

Determine weather or not the following series converges or diverges. sum[k=1,inf] 2/(k^2-1) I applied the limit comparison test with 1/k^2 2* lim k->inf [ 1/(k^2-1) ] /(1/k^2) = 2*lim k->inf k^2/(k^2-1) =H 2 then because sum[k=1,inf] 1/k^2 is a convergent p-series then...

Hello, so I've been having lots of trouble with a math problem. I can differentiate functions but I'm kinda confused on what to do when it is like y=4 So say you have the given: y= x^2 and then y=4, x=0, x=2. Rotate about the y-axis. I'm know you have to get it into respect to y so...

State if the following series converges or diverges sum[k=1,inf] cos(k)/(k^2+1) I applied the convergence test lim k->inf cos(k)/(k^2+1) =H lim k->inf -sin(k)/(2k) =H lim k->inf -cos(k)/2 = some undefined value bounded by -1 and 1 =/= 0 so the series diverges by the divergence test. I guess my...

Let: 1) P be one place operation 2) H be two place operation 3) G be two place predicate 4) k, m be two constants Let : The following assumptions : 1) \forall x [\neg G(x,k)\Longrightarrow G[H(P(x),x),m]] 2)\forall x\forall y\forall z[G(x,y)\Longrightarrow...

Homework Statement Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than 10^-5. Although you do not need it, the exact value of the series is given. ln(128) = 7*sum[k=1,inf] of (-1)^(k+1)/k Homework Equations [b]3...

Homework Statement Find the sequence of partial sums {S_n} and evaluate the limit of {S_n} for the following series .9+.09+.009+... What is .9+.09+.009+... equal to? Homework Equations The Attempt at a Solution For the first part of the question (find the sequence of...

Homework Statement Consider the following convergent series. Then complete parts a throw d below. sum[k=1,inf] 5/k^7 a. Find an upper bound for the remainder in terms of n Homework Equations Estimating Series with Positive Terms Let f be a continuous, positive, decreasing...

Homework Statement One model for the spread of rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. i) Write a differential equation that is satisfied by y ii) Solve the...

Homework Statement ∫cos^3(x)dx Homework Equations http://college.cengage.com/mathematics/larson/calculus_analytic/8e/students/derivatives/derivative_integrals.pdf http://college.cengage.com/mathematics/larson/calculus_analytic/8e/students/trig_review/trigonometry.pdf This is the...

Hello I am having calculus 2 at university in my country ( portugal ). The topics are basically double and triple integrals all the way through stokes. Do you guys have any advice on a book that could help me study this course? Thank you very much and I am sorry about my english

Homework Statement Given F(2)=5, F'(2)=6, F(4)=3, F'(4)=6 and G(3)=6, G'(3)=3, G(4)=2, G'(4)=1 A. H(4) if H(x)=F(G(x)) = ? B. H'(4) if H(x)=F(G(x)) = ? C. H(4) if H(x)=G(F(x)) = ? D. H'(4) if H(x)=G(F(x)) =? E. H'(4) if H(x)=F(x)/G(x) =? Homework Equations My teacher did not teach...

Homework Statement What is the derivative of f(x) = cos^5(sin(8x)) Homework Equations trig, product rule, chain rule The Attempt at a Solution f(x) = cos^5(sin(8x)) Answer: 5-sin^4(cos(8x))(8)

Homework Statement What is the derivative of f(t) = te^(2-7t) Homework Equations We would use product rule and chain rule, I believe The Attempt at a Solution (t)(e^(2-7t) (1)(e^(2-7t)(-7) answer: -7(e^(2-7t))

Hello everyone! Alright, my current high school math class is IB Higher Level Mathematics. It's a two year long course. During the first year we have focused primarily on Advanced Algebra, Trigonometry, and we are about to start Vectors. Year 2 consists of Calculus I, Statistics, and then...

Hi all! I'm starting Calculus 2 this Spring at my college and I was wondering what to look out for. Any specific series or problems that might be a headache? What do you suggest I prepare "better" for? Thanks for your time!

This was already posted by someone else but an answer wasn't received so I thought I'd repost. Any help is appreciated. Homework Statement Use the Maclaurin series for cosx and the Alternating Series Estimation Theorem to show that \frac{1}{2} - \frac{x^2}{24} < \frac{1-cosx}{x^2} <...

I bombed my first test this semester and had to withdraw from my calc 2 class because I did not want to get below a B for the class. Before next semester starts I would like to get a lot of practice in and I was curious if there were any websites or books that people recommend that just have...

Hello all! As it turns out, I have a condition that requires me to not be at a physical university this semester, but I would like to try and catch up a bit and also need to make my time off more productive. I would like to take a couple of math courses, particularly Calculus 2 and...

Hey I just finish Essentials Of Calculus. I'm going to take Honors Calc 1 in the fall. I just wanted to know what is in Calculus 2? I heard there are a ton of formulas to remember. lol

As a sophomore in college, I looking to take a calculus 2 course over the summer to fulfill requirements for course credit. I'm looking for online courses. I just haven't been able to successfully find a place that offers Calculus 2 online. Searching online has just been so confusing. Also...

Hey, I'm wondering if anyone knows of great self-study books on Calc 2 and 3 that give many examples and questions. Thanks