Defenition : $\cos(z)= \frac{e^{iz}+e^{-iz}}{2}$ Evaluating: $$\cos(i\ln(2-\sqrt{3}))=\frac{e^{-\ln(2-\sqrt{3})} + e^{\ln(2-\sqrt{3})}}{2} = \frac{1}{4-2\sqrt{3}} + 1 -\frac{\sqrt{3}}{2} = 2$$ ...

You've done the right move. Then since $$\frac{1}{u(u+4)}=\frac{1}{4u}-\frac{1}{4(u+4)}$$ You can get the answer $\dfrac{t \ln 2 - \ln (2^t+4)}{4 \ln2}$

Since there are n circles, angle $\theta = \frac{2\pi}{n}$(Complete angle should be $2\pi$). Let's now look at red triangle. Since it's isosceles, its median and angle bisector is the same line. So ...

It's possible to write down the antiderivative as some special function (in particular 2F1 hypergeometric function), but you don't need to evaluate the integral to prove it doesn't converge Hint: ...

$\{x_n\}$ converges $\Leftrightarrow$ $\forall \epsilon > 0 \exists n_0 : \forall n,m > n_0 |x_m - x_n| < \epsilon$. Then $\{x_n\}$ diverges $\Leftrightarrow$ $\forall \epsilon > 0 \ \... View answer 1 votes Ok, if$x<11$AND$y<11$you can sum it into$x+y<22$, but if its OR you have a complex, not a system, you can't sum it(even it would be eqs). For example, x=13 or y=2 doesn't mean x+y=15. View answer 0 votes I will try to complete the answer, mostly answering the follow-up question Rakesh Adhikesavan asked comments. Indeed if we consider$A,B,C,D\in M_n(\mathbb{R})$with block matrix$P$being$n\times n$... View answer 0 votes For$x^2 < 71, 50$is not a square. So now we take$x^2 = 71 + 50$and it turns out$11^2 = 121 = 50(\mod 71)$View answer Accepted answer 0 votes Area of integration:$x\in[\lambda;0], \lambda\in(-1;0)$. Indefinite integral:$\int \frac{x^2 dx}{\sqrt{1+x^3}} = \frac{2}{3} \sqrt{x^3+1} + C$. Using FTC:$\int\limits_{\lambda}^{0} \frac{x^2 dx}{...

Hint: try $t=\sqrt{u}$ and $dt=\frac{du}{2\sqrt{u}}$

If $a<0$ you can consider it as $-|a|$ since $|a|$ is absolute value(like unsigned value). So $a=-|a|$, and $|a|=-a$ Example: $a=-1$, $|a|=1=-(-1)=-a$

$x-2y+0z=0$ http://www.wolframalpha.com/input/?i=plane+x%3D2y $\vec{n}=\{1,-2,0\}$

Ok, i will try to give my solution. Tell me if i'm right/wrong/unproofed. $$\left\{ \begin{array}{c} \dot{x}x+t=0\\ 1+\dot{u}+\dot{y}=0\\ \end{array} \right.$$ Then since $y'=\frac{dy}{dx}=\frac{... View answer 0 votes$z(t\in[t_0;t_1])\in\mathbb{R}$and to figure out that it's continuous,$z \in C^0(\mathbb{T})$, where$T=[t_0;t_1]$. If u want to use arrow it should be Dom(z) on left side. View answer 0 votes As best I understand the question, it's about how to transpose a matrix around its secondary diagonal. If I'm right, it might be something like this:$I^{T^{*}}=I_0A^TI_0$, where$(I_0)_{ij}=\delta_{n+...