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...
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...
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}...
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.
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.
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.
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)
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...
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.
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 -...
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) +...
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...
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} -...
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.
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...