Recent content by yanjt

ooohhhh yeah!y i didnt think of tat?:confused: tat's a faster n easier way to do it!thanks!:smile: but is integrate 1/cosh x = 1/sinh x?can i jus integrate like tat? i know tat i can't jus leave cosh(arcsinh x) as my final answer.tat's y i m stucked in this step. but i will try to change it...

Thanks, dick n tiny-tim!:smile: I did it in this way: x2/√(x2+1) = √(x2+1) - 1/√(x2+1) Integrate 1/√(x2+1) = arcsinh x For √(x2+1),i subsitute x=sinh t. So, integrate √(x2+1 = cosh2t dt = 1/4 sinh 2t + t/2...

Hi, the question is integrate x^2 /square root (x^2 +1). I tried to do it but i was stucked in the very last step.at the end,I got x/2 * cosh(arcsinh x) + 1/2 * arcsinh x - arcsin (square root (x^2 + 1)) +C. I dunnoe how can I simplify cosh(arcsinh x) into simplier form in term of x. I hope...

So there is no limit for this question?I can just write the statement out without showing any working?

Hi, I am wondering whether i answer the question correctly. The question is,either find the limit of explain why there is no limit exists as k goes to infinity for k sin(k\pi/3). My answer for this question is that there is no limit exists since infinity multiply by any number will...

Hi,I have no idea on how to begin with this question.The question is: Prove that (n+a)!/(n+b)! ~ na-b as n goes to infinity.There are clue given that we can use Euler's limit and Stirling's formula to solve this question.Can you please give me some hints on how to start with this question...

Hi,I have a question like this : Determine whether the given set of vector spans M2,2 {(5 3;0 0),(0 0;5 3),(6 -1;0 0),(0 0;6 1)} I wonder can I jus directly prove that a(5 3;0 0)+b(0 0;5 3)+c(6 -1;0 0)+d(0 0;6 1) = (5a+6c 3a-c;5b+6d 3b+d) is also a M2,2 and hence,it is a vector sets...

Hi, I do not understand why it is not closed under matrix addition.It is still a Mn,n matrix isn't it?

Hi, I would like to know why the set of all n*n matrix whose determinant is zero is not a subspace of Mn,n .Can anyone explain the reason for me? Thanks!

Nothing is wrong using contradiction.What i mean is that,i wonder if proof "if n is odd,n^2 is odd" is a kind of contradiction?

Prime number is number that can be divided by or itself. if i prove that an integer is odd,its square is odd,I am not using contradiction to prove it,right?I can show that if an integer is odd,its square is odd.Yet, how can i show that if the square of an integer is even,the integer itself is...

Hi, I have no idea on how to start to do this question. If the square of an integer is even,then the integer itself is even I try to check some books but i can't get any similar examples.I wonder if I can directly prove the n=2k, n^2 = 2(2k^2). Thanks!

hi,i read the post of sq root of 2 + sq root of 3.i understand tat i should use contradiction to solve it.yet,i stuck halfway when i tried to solve it. sq root 2 + sq root 3 = p/q 2 + 2*sq root 6 +3=p^2/q^2 5+2*sq root 6 = p^2/q^2 wat should i do after this?i hav to prove that the addition...