Recent content by Cpt Qwark

The denominator is somehow supposed to be cos^{4}θ, not cos^{5}θ. That's all I need help with, nothing else.

Yeah it was a typo...

Not too sure what you mean by that. For functions with the form \sqrt{a^2-x^2} you can express them as x=asinθ

So what is wrong with this: [tex]\int{\frac{sin^{2}θ}{(cos^{2}θ)^\frac{5}{2}}}dθ= Yeah I forgot to type that in, anyway it's trig identity I'm kinda having trouble with atm.

Homework Statement Evaluate \int{\frac{x^2}{(1-x^2)^\frac{5}{2}}}dx via trigonometric substitution. You can do this via normal u-substitution but I'm unsure of how to evaluate via trigonometric substitution. Homework EquationsThe Attempt at a Solution Letting x=sinθ...

Homework Statement How does P(-1<Z<1) equal to 1-2P(Z>1)? (So you can find the values on the Normal Distribution Table) Homework EquationsThe Attempt at a Solution I tried P(-1+1<Z+1<1+1) but ended up with P(1<Z+1<2).

Yeah sorry turns out it was mistook for another expression. Anywas, what I meant was I had trouble rewriting the taylor/maclaurin series with a summation notation (Σ). Are there supposed to be patterns that you're supposed to recognise (such as the negative sign for sine and cosine functions) or...

Expanding the series to the n^{th} derivative isn't so hard, however I'm having trouble with the summation. Any tips for the summation? e.g. taylor series for sinx around x=0 in summation notation is \sum^\infty_{n=0} \frac{x^{4n}}{2n!} Thanks.

say for example when I calculate an eigenvector for a particular eigenvalue and get something like \begin{bmatrix} 1\\ \frac{1}{3} \end{bmatrix} but the answers on the book are \begin{bmatrix} 3\\ 1 \end{bmatrix} Would my answers still be considered correct?

What would be a good way to prepare for a final linear algebra exam (vectors, planes, matrices) where every question is asking for a proof? Thanks

So implicitly differentiate cos(xy)+e^{x}y=2? I got something along the lines of \frac{dy}{dx}=\frac{ysin(xy)-ye^{x}}{-xsin(xy)+e^{x}}.

Homework Statement f(x,y)=cos(xy)+ye^{x} near (0,1), the level curve f(x,y)=f(0,1) can be described as y=g(x), calculate g'(0). Homework Equations N/A Answer is -1. The Attempt at a Solution If you do f(0,1)=cos((0)(1))+1=2, do you have to use linear approximation or some other method?

Homework Statement For f(x,y)=x^2-xy+y^2 and the vector u=i+j. ii)Find two unit vectors such D_vf=0 Homework Equations N/A. The Attempt at a Solution Not sure if relevant but the previous questions were asking for the unit vector u - which I got \hat{u}=\frac{1}{\sqrt{2}}(i+j) for the maximum...

Homework Statement \begin{array}{rrr|r} -1 & 2 & -1 & -3 \\ 2 & 3 & α-1 & α-4 \\ 3 & 1 & α & 1 \end{array} α∈ℝ for the augmented matrix, what value of α would make the system consistent? Homework Equations N/A Answer: α=2 The Attempt at a Solution I know that the system has to have an...

Homework Statement Given the matrices A, B, C, D, X are invertible such that (AX+BD)C=CA Find an expression for X. Homework Equations N/A Answer is A^{-1}CAC^{-1}-A^{-1}BD The Attempt at a Solution I know you can't do normal algebra for matrices. So this means A≠(AX+BD)?