Recent content by kira137

Homework Statement I was given | 1 2 -1 2 | | 2 4 1 -2 | = A | 3 6 0 -6 | and reduce it to rref. Also I had to find all four fundamental subspaces of A. 2. The attempt at a solution so I did R2 - 2R1 R3 - 3R1 R3 - R2 and got | 1 2 -1 2 | | 0 0 3 -6 | | 0 0 0 -6 |...

Homework Statement Find limit ...(1-cos(2x^2)) / (1-cos(3x^2)) x->0 2. The attempt at a solution since the above gave me 0/0, I used l'Hopital method.. then i got (4x)sin(2x^2) / (6x)(sin3x^2) which gives me 0/0 again.. so I kept on using l'Hopital.. but it seemed on going...

\quad \sum_{n=1}^\infty \frac{1}{n^2} &= \frac{\pi^2}{6}. \end{alignat*} um how did you get pi^2/6..?

ohh! wow thank you so much! I think I understand.. I thought all sums had a final number because I guess prof always used an example that gave number for result.. thank you again

since it goes to infinity, it diverges.. I think.. so for my question above, since it goes to invinity, it diverges also?

\lim_{n\to\infty} \ln(n-2) wouldn't this be infinity?

oh i see.. then how would I find if it converges or diverges? I think i remember prof cancelling a bunch of terms by dividing it by some number.. is this the way to do it?

i understand that part.. but I don't understand how I would use that to solve a question, how do I look for a final sum if the number keeps going on forever?

Homework Statement n=3, where it goes to infinity \sum ln(n-2) 2. The attempt at a solution I'm not even sure how to start.. I just learned this today and I didn't understand this.. so I started solving questions from text then came across this question (didn't have an answer in the...

Homework Statement S dx/(1-x^2)^(3/2)Homework Equations The Attempt at a Solution I tried seperating the bottom S 1/((1-x^2)^(1/2))(1-x^2) then tried to use integration by parts... but I think that doesn't work.. how would I get the power to 1/2? thank you in advance

Thank all of you for your help. I haven't learned partial fractions yet so I tried Bohrok's way by letting x^2 = u This is what I got for answer: arctan(-x^2) is it right? I had trouble with solving 1/(1-u^2).. so i just did integral to tan, am I allowed to?

Homework Statement Evaluate the following: Integral of 2x/(1-x^4) dx with lxl<1 The Attempt at a Solution I tried to use long division to solve the question, then got: 2x/(1-x^4) = (2x^5)/(1-x^4) + 2x S (2x^5)/(1-x^4) + 2x dx this is where I seem to be stuck on.. do I...

My instructor mailed the class saying that the actual answer is 169(pi)/42. I appreciate you going over the question, thank you!

Homework Statement Evaluate using the cylindrical shell method, the volume of the solid of revolution obtained by rotating the region enclosed by the curves y=x^3, y=-x and y=1 around the line y=-1. The attempt at a solution The answer is suppose to be 127(pi)/42 but I keep getting...

Homework Statement Find the length of the curve x^(2/3)+y^(2/3) = 1 for x in the interval [0.1]. The attempt at a solution y = (1-x)^(2/3) f'(x) = (4x^(-1/3) (1-x^(2/3))^(1/2))/9 then i plugged it into arc length formula 1 S sqrt(1+((4x^(-1/3) (1-x^(2/3))^(1/2))/9)^2 = 0 1 S...