# Search results

1. ### Simplifying an ODE into explicit form

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} -...
2. ### Comp Sci FORTRAN 90 Help- reading input in format DDMMYYYY + more

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...
3. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

WOW! Thank you so much for helping and putting up with me!
4. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

well, pi/2 for positive multiples of i or I am > 0, or -pi/2 for negative multiples of i, or I am < 0

pi/2, right?
6. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

-pi/2! but how do i go from (2bi)/(2a+1)? do i just ignore the (2b/2a+1)?

pi/2!

or pi/2
9. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

OMG, i forgot you said in relation to the x axis. 90 degrees. *hits head*
10. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

Isnt i on the y-axis? which would make the angle 0.
11. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

I don't know. You make it sound so simple, but I am so confused. I am sorry. arcsin(Im(z)/|z|)?
12. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

I don't know what "c" is, am i supposed to come up with a number? Does ci = sinθ?
13. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

"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| ."
14. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

Are you still there? I am so confused.
15. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

0? My textbook barely even touches on the argument, that's why I am so lost.
16. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

How do i do that with 2b and 2a+1?
17. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

Wow, I am shocked i remembered that lol. It would equal 2bi/(2a +1). Thanks for helping me through it btw.
18. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

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.
19. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

Ok, i get: (a2+b2+2bi-1)/(a2+b2+2a+1) Is that right?
20. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

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?
21. ### Complex Analysis - Value of Arg[(z-1)/(z+1)] between -pi and pi

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)...
22. ### Approximation of continuous functions by differentiable ones

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.
23. ### Approximation of continuous functions by differentiable ones

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...
24. ### Show that the following function is Riemann integrable.

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...
25. ### Analysis help - Continuous function that is differentiable at all points except c

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.
26. ### Analysis help - Continuous function that is differentiable at all points except c

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) =...
27. ### Algebra help - primitive roots and minimal polynomials

That makes sense, but from what i thought i understood, the n is usually the order (or degree) of the polynomial. But i might be wrong.
28. ### Algebra help - primitive roots and minimal polynomials

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
29. ### Algebra help - primitive roots and minimal polynomials

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...
30. ### Prove the following limits when c ∈ N (analysis help):

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.
31. ### Prove the following limits when c ∈ N (analysis help):

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.
32. ### Prove the following limits when c ∈ N (analysis help):

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...
33. ### Abstract algebra-> Let R be a ring and let M2(R) be the set of 2 x 2 matrices with

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. De fine a function f by: f(r) = (r 0) <----matrix ...(0 r) for any r ∈ R (a) Show that f is a...
34. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = 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.
35. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = a

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?
36. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = a

Nothing, but you put a doubt in my mind, and now I am not sure if I am missing something.
37. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = a

So what am i missing, it seems right to me. I am starting to get frustrated with the question :S
38. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = a

Havent i showed that? I show that a is the least upper bound of S, so any other upper bound has be greater or equal to a.
39. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = a

What about the proof i posted above, also no good?
40. ### Find the supremum and infimum of S, where S is the set S = {√n − [√n]}

Can i use a limit to prove sup S = 1, since 1 isn't contained in the set?
41. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = a

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...
42. ### Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

Thanks sooooooo much :)
43. ### Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

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?
44. ### Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

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?
45. ### Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

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.
46. ### Show that if a ∈ R, then: sup{r ∈ Q : r < a} = a

You guys lost me. Can somebody please explain? I am really trying to learn this, my textbook sucks!
47. ### Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

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))?
48. ### Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

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?
49. ### Find the supremum and infimum of S, where S is the set S = {√n − [√n]}

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...
50. ### Show that if n belongs to N, and: An: = (1 + 1/n)^n then An > An+1 for all natural n

Ok, i get r = -1 / (n^2 + 2n + 1 ), so then what would be my inequality? [1 -1 / (n^2 + 2n + 1 )]^ n >= ?