Calc 2 Definition and 95 Threads

My work so far: I am stuck because when I inputted the two possible values of t and k, neither solution worked. Where did I go wrong? Pointers would be appreciated! :)

Hi! I am having trouble finalizing this problem. The interval is given so we know that a = 1 and b = 2. From there you can figure out that ∆x = 1/n, xiR = 1 + i/n. Using logarithmic properties, I rearranged the expression and wrote (1 + i/n)(1/n)ln[(n + i)/n]. I can guess that the function is...

Is there a way to solve a Disk,Washer,Shell method problem without actually creating a graph?

A0 = 1 A1 = 3 3(An-1) / 4(An-2) = An

An open tank has the shape of a right circular cone. The tank is 8 feet across the top and 6 feet high. How much work is done in emptying the tank by pumping the water over the top edge? (The weight-density of water is 62.4 pounds per cubic foot.)

Homework Statement Consider a trough with triangular ends, as pictured below, where the tank is 10 feet long, the top is 5 feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water of weight density 62.4 pounds/ft^3. How much force does the...

Homework Statement (summation from 1 to 100) Σ (1/k) - (1/(k+1)) [/B]Homework Equations Σc = cn Σi = (n(n+1))/2[/B]The Attempt at a Solution I can only find summation equations for variables in the numerator. I'm not sure how to even start this problem. [/B]

Homework Statement Please help me solve the calc problem pictured! Homework Equations y=3-x^2 and y=x+1 The Attempt at a Solution My attempt is in one of the photos!

Homework Statement Please look at the photo! Homework Equations -x^2+4x=x^2-6x+5 The Attempt at a Solution I got 2x^2-10x+5 but it says it's wrong

Took the calculus 2 exam yesterday. 30 question exam. Was on a roll from questions 1-18 I think k only had one unanswered at that point, the test got harder and harder and once I hit question 20 I felt pretty defeated. Once I got to the questions asking about finding volume and surface area of...

Homework Statement [/B] There are three problems that I am struggling with. 1. ∑[k2(x-2)k]/[3k] 2. ∑[(x-4)n]/[(n)(-9)n] 3. ∑[2k(x-3)k]/[k(k+1)] The Attempt at a Solution On the first two I am having problems finding the end-points of the interval of convergence. I use the ratio test. 1...

I am taking calc 2 online, and am currently finishing the part on "Strategy for Integration", where all the u-sub/trigsub/partial fraction/by parts are combining into a problem set. They were already challenging on their own, but combining all these is very tricky haha! Definitely not high...

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...

I'm in a bit of a dilemma. At my university, Calc 2 is a prerequisite to Linear Algebra. However, I have been told that it's totally doable to take both at the same time. What do you guys think? Do most universities wave this requirement if you take them concurrently? Thanks!

I want to major in computer and electrical engineering physics. I don't actually know much about the specifics, but I've been an electrical engineering hobbyist since high school, I built my own desktop computer and enjoy programing in C++, and I study some physics in my free time. All I know is...

Homework Statement Find the Taylor Series for f(x)=1/x about a center of 3. Homework EquationsThe Attempt at a Solution f'(x)=-x^-2 f''(x)=2x^-3 f'''(x)=-6x^-4 f''''(x)=24x^-5 ... f^n(x)=-1^n * (x)^-(n+1) * (x-3)^n I'm not sure where I went wrong...

I'm going to have a gap between math classes at some point. I can either take calc 1, then calc 2 the following semester, then have a semester gap with no math, and then calc 3. Or calc 1, no math gap, calc 2, calc 3. The reason I am asking is because i will forget some information in the...

Hey everyone, I am winding down of finals next week, and will be off of school for a month. I was planning on beginning Calculus 2 over winter break to get a head start, and I don't want to lose the information I've already learned. We left off on U-Substitution on some basic integrals. I was...

Hey guys, this one is just for funnsies. So when dealing with an alternating series test, 3 requirements must be met, : Alternating u(sub n) ≥ u(sub n+1) for all n ≥ N, for some integer N u(sub n) → 0 as n → ∞. So I have been coming up with examples where of these are true, and one isnt. A...

Homework Statement Find integral of 4*e^(4x)*sin(e^(4x))dx Homework EquationsThe Attempt at a Solution Can I do this in this math problem I took the integral of 4e^(4x)*sin(e^(4x)) dx using substitution method. in the end I got e^(4x)*-cos*[1/e^(4x)] do the ex^4x just cancel out?

hey everyone so i just took my calc 2 exam and the whole class basically bombed it. the professor is giving us a chance to retake the exam or to keep the score we had the first time around. the exam is on integration by parts, trig sub, trig integrals and partial fractions decomposition. i got a...

1. I need help solving this integral, I've tried using trig substitution, but I'm getting nowhere with it. ∫x/(6x-x^2)^3/2dx Like I said before, I tried changing the bottom to a radical and trig substituting but it doesn't seem to get me anywhere. Thanks in advanced for any help.

How difficult will this be? I have 6 semesters left at CC and I need to take college algebra, precalc, calc 1, calc 2, calc 3, linear algebra, and dif equations. So I have to have some overlap somewhere but I am not 100% sure. College Algebra is a prereq for precalc, which I have to take...

Hi, I'm teaching my self Calc 2 at the moment and made an equation that I want to integrate: \frac{1}{x*\phi^{1-cos(2*\pi*x)}} (phi is just a really large constant) I'm not asking anyone to do it for me, but am curious if this is something I can even hope to be able to integrate with...

Ello every one, i have interesting question. Any one who has james stewert 7th edition calc book I am on secotion 8.1 studying for an exam. number 13 of 8.1 says this y= ln(secx) find arc length from 0-pi/4 here is what i do first in my opinion. y`= 1/sec(sectan) y`= tanx...

[solved]Find volume of solid generated (Calc 2) Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y=e^x, and the line x = ln 2 about the line x= ln 2. So I tried graphing it to see visually, and the expression I got...

University physics with lab general chemistry 2 with lab Design class linear Algebra Culculs 2. Does this look like an overload? At times it feels like it is and at times it feels like it can be done. the mechanics course and the general chemistry course both come with labs which is the...

A solid lies between planes perpendicular to the x-axis at x=-a and x=a for values of a>0 to be given below in parts (i) and (ii). In each case the cross-sections perpendicular to the x-axis between these planes run from the semicircle y=√(a^2-x^2) to the semicircle y=-√(a^2-x^2). If...

This isn't homework, It is just book problems that I am practicing, I am checking some answers with wolfram and others with the book answers. Homework Statement \begin{align} \int \frac{sin(w)\,dw}{\sqrt{1-cos(w)}}\\ \end{align} Homework Equations I used u substitution... Not sure if I...

My first post let's see if i did this typing right, if not please forgive me... Homework Statement \int \frac{(1+ln x)^2}{x}\,dx Homework Equations Trying to attack it by using substitution.. The Attempt at a Solution Using... u = 1 + ln(x) , du = 1/x \begin{align} \int \frac{(1+ln...

im in calculus 2 right now and we are doing differential equaitons right now. I am confused as to why when i find the integrating factor I(x)=e^(∫p(x) and when i multiply both sides i get e^∫(p(x))[(dy/dx)+p(x)*y]=d(e^(p(x)dx)*y) how are they equal. i will give an example. (dy/dx)+y=x*e^(x)...

Homework Statement Carrying capacity N of a population Assume: small population, dp/dt is proportional to P if 0<P<N then p(t) increases if P>N then P(t) decreases equilibrium means dp/dt = 0 Homework Equations dP/dT = KP(N-P) Solve for P(t) The Attempt at a Solution...

Homework Statement Ok, so I have the problem, and I have the answer, but I don't know how they arrived at the answer. I'll show you the problem, and what I tried and maybe somebody can point out where I am going wrong, or some hints to put me on the right path. (2x-1)/(x+1) being integrated on...

Hello, I am a student at a CC currently taking Calculus I and Intro to Chem (never had chem in high school). I have high A's in both. I would like to major in Mechanical Engineering. I was hoping to get some advice from people who have tried this schedule: Calculus II Physics I (Calculus...

Homework Statement The definite integral of ∫(x^2 √(a^2-x^2) dx from 0 to a Homework Equations The Attempt at a Solution So i don't need actual help with this problem. I got the answer, (π*a^4)/16 and I verified with the back of the book. The question I have is whether this...

Homework Statement "The base of a solid is the region enclosed by y=4-x^2 and the x-axis. Find the volume of the solid if cross-sections perpendicular to the y-axis are isosceles right triangles with hypotenuse in the base" I think she forgot to add to rotate the equation around the y-axis...

Homework Statement \int(x^2-2x+3)dx/(x^3-x^2-x-2) Homework Equations Trig substitution/ partial fractions? The Attempt at a Solution I used partial fractions to reduce the integral down to: \intdx/(x-2)+\int(x-1)dx/(x^2+x+1) The first integral is easy enough, but the...

Homework Statement Find the radius of convergence and interval of convergence of the series: \sum (-1)n * ( x^(2n) / (2n)! ) for n=0 to infinity Homework Equations well, any of the divergence tests: ratio, limit comparison, etc. The Attempt at a Solution I don't get power...

Hi, I've been debating with myself if I should pass out of calculus 2 by an exam or I should take the full semester. I am currently taking calc 1 this semester. Is there a pro or a con to either of these routes? I also would need to brush up on certain calc 2 topics since I have not taken...

Hi, Has anyone taken calc 2 at a CC in the summer? I'm thinking of doing it so I can get to calc 3 faster. I'm worried that it might be too fast and I won't be able to absorb the material which will prepare me for calc 3. If this is too vague, I'll elaborate ;). Thanks, S

Interesting Telescoping Series -- Calc 2 My problem with this series arose when I attempted a partial fractions decompisition of the following, (k-1)/(2^(2k+1). I attempted to factor the denominator with 2(2^k) which is right, but where do I go from there? It does not help much to multiply...

Homework Statement ∫ from 0 to 1 of 1/sqrt(4-x^2) dx I know from Wolfram Alpha that the answer should be π/6, and that the indefinite integral would be arcsin(x/2). I see the connection between this and the antiderivative of arcsin, I'm just not sure how to handle the 4 rather than the...

I've had to take a handful of prerequisites for Math and it's caused my academic schedule to get jacked up - To keep a full-time load in each semester I will have to take Calc2(4 credits) and Engineering Physics 1(4 credits) during next summer (eight week session). It would be a Mon-Thursday...

I don't remember ANYTHING from this section when I took Trig but we're finding the area of curves in the polar coords. Looking at the book they give us this equation r=2cos3\theta I can see, and I know how to figure out its a 3 leaf "rose" symmetrical about the theta= zero axis, but I can't...

Homework Statement Sketch a graph of the polar curve whose points satisfy the following: As theta increases from 0 to pi/2, r decreases from 4 to 2. As theta increases from pi/2 to pi, r decreases from 2 to 0. As theta increases from pi to 3pi/2, r decreases from 0 to -1. As theta increases...

I am really starting to doubt myself, which sucks because it's what I want to do. Should I retake? Can I move on and be ok? (I did fine in the integrating part, but not so much in series/sequences)

Homework Statement Calculate the fluid force of a right triangle with height 3ft and base 2ft submerged in water vertically and it's upper vertex at a depth of 4ft. Homework Equations F = w int(from a to b) y*f(y)dy The Attempt at a Solution I'm just not seeing how to set this...

Hey everyone! My name is Ben, I'm a senior in high school working on an BC Calc problem and am having some general questions about it. The question reads: Let f be a function defined on the closed interval [-3,4] with f(0) = 3. The graph of f', the derivative of f, consists of one line segment...

Hey everyone. I'm planning on taking calc 2 this semester in addition to some other demanding courses. Since I'm hoping to at least minor in physics, I know the class is important for later and I will take it seriously. However, I'd like to take it pass/fail to make this semester much less...

Homework Statement I have stared at this too long and do not know which test to approach it with, even writing it out. The problem is State the Convergence or Divergence of the given series: Summation n=1 to Infinity of 1 / sqrt (n^3 + 2n) Homework Equations I narrowed it down to...