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?
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)?