# Search results for query: *

1. ### Absolute convergence: ratio/root test n/n^n

Thanks for mentioning the typos, I see them. I meant to say I applied the ratio test first, and the exponent in the denominator of my first line should be n+1. I remember the limit from deriving it with L'Hopital's rule, 1/e. Thanks, I simply didn't see I could reduce it by dividing by...
2. ### Absolute convergence: ratio/root test n/n^n

Homework Statement Doing some problems from textbook, I need to determine whether the series is absolutely convergent, conditionally convergent, or divergent. n!/n^n I plugged it into WA, and it says the series doesn't converge, but I'm not sure how to figure it out. Homework...
3. ### Series problem: given s(sub n), find a(sub n) and sum of a(sub n)

Homework Statement This is a problem in my book, and the answer is in the back. Unfortunately I can't solve it. If the nth partial sum of a series \sum a_{n} n=1 to infinity is s_{n} = (n - 1) / (n + 1) find a_{n} and \Sigma a_{n} n=1 to infinity Homework Equations a_{n} = s_{n} - s_{n-1}...
4. ### Integration w/ trig. substitution (x^2 + 1) / (x^2 - 2x + 2)^2

why is it always so obvious after the fact :p thx
5. ### Two undetermined constants

v(1)=24, which means t = 1. Plug in 1 wherever you have a t.
6. ### Two undetermined constants

You don't. You just reused the same variable. I rewrote it: v(t) = 12t^2+6t + C s(t) = 4t^3+3t^2 + Ct + D v(1)=24 s(0)=0
7. ### Darivative problems which one is wrong?

For the last one, it might be easier to write it out as. f(x) = pi x^-2 Find the derivative, see if it matches. For the 3rd, try out a few other possibilities. You should point out to your teacher that when a=e, that e^x works.
8. ### Two undetermined constants

yes, but C is not the same value or variable in both of those equations. C is just commonly used to represent an unknown constant. The C in your first equation will be the K in your 2nd equation.
9. ### Two undetermined constants

If I'm understanding your use of variables correctly, K is C. K is one of the coefficients in s(t), which is known by figuring out C in v(t). v(t) = ... + C s(t) = ... + Kt + ... You wrote v(t) correctly, now just plug in t=1, and you'll get C.
10. ### Two undetermined constants

You need the constant, so it's v(t) = 12t^2+6t+C to find C, you plug in the fact that you know v(1)=24 After you find C, then you repeat the process to find s(t)
11. ### Two undetermined constants

Someone's been skipping class. Anti-derivative is basically doing the reverse of a derivative. For example the derivative of 3x^2 + 5x + 4 = 6x + 5 The anti-derivative of 6x + 5 = 6x^2 * (1/2) + 5x * (1/1) + C = 3x^2 + 5x + C If the f(x) = 3x^2 + 5x + C and we're given f(0)=4 then we can...
12. ### Two undetermined constants

Find the anti-derivative of a(t), which is v(t). Plug in t=1 for v(t) to get the constant. The find the anti-derivative of v(t), which is s(t). Plug in t=0 for s(t) to get the constant, and now you have your answer.
13. ### Integration w/ trig. substitution (x^2 + 1) / (x^2 - 2x + 2)^2

Another even numbered problem in my book, so no textbook answer. I checked it in WolframAlpha(WA), but the answer came out slightly different. Hopefully no typos in this writeup. Homework Statement \int \frac{x^2 + 1}{(x^2 - 2x + 2)^2}dx Homework Equations I factor the denominator: (x^2 -...
14. ### Trig integration (cos(x)+sin(x)) / sin(2x)

cool discussion guys. I just worked the integral of csc(x) on my own, and I came up with that funky version. Didn't realize it was less common :).
15. ### Trig integration (cos(x)+sin(x)) / sin(2x)

Prepping for my test, and I can't seem to solve this problem. Homework Statement \int \frac{cos(x) + sin(x)}{sin(2x)}dx Homework Equations Not sure if it led me astray, but I used the trig. property: sin(2x) = 2sin(x)cos(x) The Attempt at a Solution = \int \frac{cos(x) +...
16. ### Trig. integration tan^5(x)dx

Ah! So that means my initial answer was right (assuming I don't keep screwing up my trig), since: = tan^4(x)/4 - tan^2(x)/2 + ... + C = [sec^4(x) - 2sec^2(x) + 1]/4 - tan^2(x)/2 + ... + C = sec^4(x)/4 - sec^2(x)/2 - tan^2(x)/2 + ... + C = sec^4(x)/4 - [tan^2(x) + 1]/2 - tan^2(x)/2 + ... + C...
17. ### Trig. integration tan^5(x)dx

I'm not sure if my answer is just wrong or basically the same as the one in the back of my book. Homework Statement \int tan^5(x)dx The Attempt at a Solution My answer: \int tan^5(x)dx = \frac{tan^4(x)}{4} - \int(sec^2(x)tan(x) - tan(x)) dx \int tan^5(x)dx = \frac{tan^4(x)}{4} -...
18. ### Problem using L'Hospiital's Rule (indeterminate form: INF - INF)

I tried out all your suggestions. This is really cool. Thx everyone.
19. ### Problem using L'Hospiital's Rule (indeterminate form: INF - INF)

Homework Statement \stackrel{lim}{x\rightarrow\infty}(\sqrt{x^2+x} - x) I have no idea how to do this. In my book, it says I want to convert \infty - \infty forms into a quotient by getting a common denominator, rationalization or by factoring.
20. ### Applying inverse trig function

Hey people, first time posting. This isn't really homework, but I want to know how to apply inverse trig functions. So, while looking over some problems in my textbook, I came across the following, which I really have no idea how to do. Homework Statement A ladder 10ft long leans against a...