Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...
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2 views
conformal mapping
Prove that application ζ^-1:B^2---> H^2 is conform.
ζ^-1(x1,x2,x3)=(x1/1+x3 , x2/1+x3)
B^2 is unit disc and H^2 is hyperbolic 2-space and conformal mapping preserve angles.
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0answers
9 views
Show that unhomogeneous linear differential equation degree $n$ has $n+1$ roots independent linearity on $(a,b)$
Show that unhomogeneous linear differential equation degree $n$ has $n+1$ roots independent linearity on $(a,b)$ with coefficients in equation are continuos funtions on $(a,b)$.
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0answers
11 views
Directional derivative, tangent vector, double integrals
Let f be differentiable on the domain $D$ and let $\nabla f(x_0, y_0) = (0, 0)$. Then every directional derivative of $f$ at $(x_0, y_0)$ is $0$.
Let $C$ be a parametrized curve with ...
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0answers
14 views
Integrating a scalar function over a manifold
The following question is from Munkres' Analysis on Manifolds Section 25 question 2.
Let $\alpha (t), \beta (t), f(t)$ be real-valued functions of class $C^1$ on $[0,1]$, with $f(t)>0$. Suppose ...
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2answers
33 views
how to solve machine without calculator?
how to solve machine without calculator?
$log(x)=\dfrac{log(1,04)}{6}$
I'm not getting a solution without using a machine calculation or logarithm table.
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0answers
19 views
Finding the counting function
I'm running into a problem determining what's going on here:
There are n types of food that include bread, pizza, candy, burgers, sandwiches, pasta, etc. If George takes bread, he will have to ...
1
vote
3answers
62 views
Find dy/dx given $y = {1 \over {1 + \sqrt x }}$, using the chain rule
I've tried this:
$\eqalign{
& = {1 \over {1 + \sqrt x }} \cr
& = {1 \over {\sqrt {1 + x} }} \cr
& = {1 \over {{{(1 + x)}^{{1 \over 2}}}}} \cr
& = {(1 + x)^{ - {1 ...
3
votes
1answer
33 views
Proving that a critical point is a minimum
I am solving a problem, which is
"Find the point of the paraboloid $P:=\{(x,y,z)\in\mathbb{R}^3 | x^2+y^2=z\}$ which is the nearest to the point $(1,1,\frac12)$."
I have already determined (using ...
3
votes
0answers
19 views
Basic computation of a double graded spectral sequence: $^I E^0_{pq}$
Let $C=\oplus_{p\geq0, q\geq0}C_{pq}$ be a double graded group with two differentials: $d^I_{pq}:C_{pq}\rightarrow C_{p-1,q}$ and $d^{II}_{pq}:C_{pq}\rightarrow C_{p,q-1}$, with the usual assumption ...
3
votes
1answer
33 views
For $1 \leq q < p \leq 8$, identify which $p^2 + q^2$ is not prime (Pythagorean Triples)
In my previous question: Calculating Pythagorean triples, I used
$$x + iy = (p + qi)^2 \hspace{1cm} z = p^2 + q^2$$
to calculate a load of Pythagorean triples (of the form $x^2 + y^2 = z^2$) where ...
2
votes
1answer
27 views
Find radius and interval of convergence for $\sum_{n=1}^\infty$ $\frac{5^n}{n+2^n}x^n$
Find radius and interval of convergence for $\sum_{n=1}^\infty$ $\frac{5^n}{n+2^n}x^n$
So if i apply ratio test, I get $\lim_{x\to \infty} 5|x||\frac{n+2^n}{n+1+2^{n+1}}| $
Now need help to to check ...
1
vote
2answers
33 views
If derivative $f'$ of a function $f$ satisfies $0 < C \leq f'(x)$ for all $x$ then $f$ is bijective
Proposition If derivative $f'$ of a function $f:\mathbb R\to\mathbb R$ satisfies $0 < C \leq f'(x)$ for all $x\in\mathbb R$ then $f$ is bijective.
It is clear that if there exist ...
5
votes
1answer
46 views
Question about exercise 8.5 in Jech's Set theory
The exercise I am asking about is the next one:
For every stationary $S\subset \omega_1$ and every $\alpha < \omega_1$ there is a closed set of ordinals A of length $\alpha$ such that $A\subset ...
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0answers
17 views
A Has characteristic polynomial that can be reduced to linear products $\Rightarrow$ A similar to upper triangular Matrix
Prove that if $A\in M_{n}\left(\mathbb{F}\right)$ matrix with a characteristic polynomial that can be written as a product of linear elements (?) ...
7
votes
2answers
59 views
How to find the minimum of f(x)?
I need to find the minimum of $f(x)$ with
$$f(x)=(\sin(x)+\cos(x)+\tan(x)+\cot(x)+\sec(x)+\csc(x))^2$$
Could you help me with some clues?
