Homework Statement
So i think i found the general solutions to both these separable equations, but I am not sure if I am suppose to simplify any further to get it in explicit form, and how i can even do that.
Homework Equations
The Attempt at a Solution
1. \frac{dy}{dx} -...
Homework Statement
This is assignment is on FORTRAN 90:
In an assignment i have, i am to enter a date in the format DDMMYYYY, and its suppose to compute and display the day of the week that date falls on (based on a given algorithm). I was able to code a program that would give me the right...
"Arg z, the argument of z, defined for z ≠ 0, is the angle which the vector (originating
from 0) to z makes with the positive x-axis. Thus Arg z is defined (modulo
2π) as that number θ for which
cos θ = Re z/|z|
; sin θ = I am z/|z| ."
Wow, am i rusty. I am so embarrassed to say that i don't know. I may be wrong, but i think i faintly remember a^2+b^2= 1. But i don't think its right. As for your other questions, i don't know. I am sorry, I am an idiot.
Is this what I am supposed to do:
(z-1)/(z+1) = (a + bi -1)/(a+bi +1) = (a2 - b2 +2abi -1)/ (a+bi+1)2
Is that right? If so, what do i do next, or if I am wrong, what am i doing wrong?
Homework Statement
Let Arg(w) denote that value of the argument between -π and π (inclusive). Show
that:
Arg[(z-1)/(z+1)] = { π/2, if Im(z) > 0 or -π/2 ,if Im(z) < 0.
where z is a point on the unit circle ∣z∣= 1
The Attempt at a Solution
First, i know that Arg(w) = arctan(b/a)...
No, there was no limit defined in the problem, i typed it exactly how my prof. worded it.
And you are right about my conclusion for the integral, had a brain cramp and figured that f is equal to 1, which would make my integrating very easy. So completely disregard that i said that.
Homework Statement
Let f: R-->R be continuous. For δ>0, define g: R-->R by:
g(x) = (1/2δ) ∫ (from x-δ to x+δ) f
Show:
a) g is continuously differentiable
b) If f is uniformly continuous, then, for every ε>0, there exists a δ1>0 such that sup{∣f(x) - g(x)∣; x∈R} < ε for 0<δ≤δ1
The Attempt...
Homework Statement
Show that the function f: [0,1] -> R defined by:
f(x) = 1, if x=1/k for some k
f(x) = 0, else
is Riemann integrable on [0,1]
Homework Equations
The Attempt at a Solution
I attempted the problem using Cauchy's criterion but found that this function is...
How does the f ' being uniformly continuous help me at reaching my answer? If the Interval is [a,b], then the f ' is continuous on the open intervals (a,c) and (c,b), how could i show that while f' may not be continuous at in the interval at c, a derivative still exists.
Homework Statement
Let I be an interval, and f: I --> R be a continuous function that is known to be differentiable on I except at c. Assume that f ' : I \ {c} --> R admits a continuous continuation to c (lim x -> c f ' exists). Show that f is in fact also differentiable at x and f ' (c) =...
From what i understand, a primitive root is a value that when taking to the power of the order of the polynomial, you will get 1 (mod 3 for this example) I don't know if this is right, but i get x^2+1 as a primitive root. Does that make sense. The order of the polynomial is 2, so (x^2+1)^2 = 1
Homework Statement
(a) Find a primitive root β of F3[x]/(x^2 + 1).
(b) Find the minimal polynomial p(x) of β in F3[x].
(c) Show that F3[x]/(x^2 + 1) is isomorphic to F3[x]/(p(x)).
The Attempt at a Solution
I am completely lost on this one :confused:
Homework Statement...
The question says "prove that...", but doesn't specify if i have to use epsilons and deltas or can use another theorem such as squeeze theorem, ratio theorem, etc to prove the limit.
Im confused, isn't that what i did? I removed the radical in the numerator by multiplying it by the the square root + 1, but it then leaves me with a radical in the denominator. I still don't understand how it would give me for a) a limit of 1/c.
Homework Statement
Prove that when c ∈ N:
a)
lim [\sqrt[c]{1+x} - 1]/x = 1/c
x->0
b)
lim [(1+x)^r - 1]/x = r
x->0
,where r = c/n
The Attempt at a Solution
My approach for a and b are pretty similar, i get stuck at the same point.
For a, i multiplied the numerator...
Abstract algebra--> Let R be a ring and let M2(R) be the set of 2 x 2 matrices with
Homework Statement
Let R be a ring and let M2(R) be the set of 2 x 2 matrices with entries in R.
Define a function f by:
f(r) = (r 0) <----matrix
...(0 r)
for any r ∈ R
(a) Show that f is a...
Couldnt have said it better myself, the way i usually study math is by trying some examples, looking at the answer, and then learning from it. But there are no examples to learn from. So I am having a lot of trouble understanding this class, as apposed to other math classes.
Ok i will, but if i find that i think its right, am i right, lol. I mean there must be a right answer, if i think mine is right, it doesn't mean I am right. Ok, now I am just confusing myself... Can you please just tell me if I am right or wrong, and if I am wrong ill go back and see what's wrong?
K i received help from a friend who took the course, he's not sure if he's right though.
He says that since Q is dense in R, every nonempty interval of R contains a rational.
From the definition of the set S = sup{r ∈ Q : r < a} it follows a is an upper bound of the set S. For every ε >0...
Since the right hand side is greater than 1, and the left hand side is greater than or equal to the right hand side, then the left hand side must be greater than 1. In which case, an+1 > an. Is this good?
Ok, if i multiply the entire right hand side, i get (n^3 + 3n^2 + 3n + 2) / (n^3 + 3n^2 + 3n + 1). Which is greater than 1, so does that prove that (1+1/(n+1))^(n+1)/(1+1/n)^n > 1, and therefore an+1 > an?
Right, that's what i meant to type:
(1+1/(n+1))^(n+1)/(1+1/n)^n >= (1 - n / (n^2 + 2n + 1 )^n)*(1+1/(n+1))
So what do i do next :S. I really appreciate your help by the way.
Huh? sorry you've lost me. I am not the brightest guy when it comes to this, but I am really trying to understand it. So i have:
(original-->) (1 + 1/(n+1))/(1+1/n) >= (1 - n / (n^2 + 2n + 1 ))*(1+1/(n+1))?
Yes, i have bernoullis inequality right in front of me:
(1+x)^n ≥ 1+ nx for all natural numbers.
So would it be:
[1 -1 / (n^2 + 2n + 1 )]^n ≥ 1 - n / (n^2 + 2n + 1 )
and what happens to the other 1+1/(n+1) from the original equation?
So would i be able to use the same reasoning for the supremum:
By definition of {x}, {x} < 1 since x - [x] = {x}, therefore {x} never reaches 1. So 1 is an upper bound.
Let b be an upper bound where b < 1. If you take ?, (what value would i be able to use here to prove this, since 1 isn't...