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
[/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...
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 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 Equations
The 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...
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...