Recent content by eclayj

Homework Statement Show that for a set A\subsetN, which is numerically equivalent to N=Z+, and the set B = A \cup{0}, it holds that A and B are numerically equivalent, i.e., that A \approxB Hint: Recall the definition of A≈B and use the fact that A is numerically equivalent to N. Note...

Homework Statement Determine if the sets A, B, C, and D satisfy the following proposition (p) for the set S: Homework Equations p: for all ε > 0, ∃ x \in S such that x < ε A = {1/n : n \in Z+} B = {n : n ε Z+} C = A \cup B D = {-1} The Attempt at a Solution I am...

So if I understand it right, I have the following: Let R be a relation on A. Prove that if Dom(R) ⋂ Range(R) = ø, then R is transitive. Taking the negation of the "R is transitive" to try proof by contrapositive gives the following: 1.) ∃ x,y,z ∈ A s.t. (x,y) ∈ R ∧ (y,z)∈ R...

I'm having trouble with the following: Let R be a relation on A. Prove that if Dom(R) \bigcap Range(R) = ø, then R is transitive. I took the negation of the "R is transitive" to try proof by contrapositive (as the professor suggested), and have the following: \exists x,y,z \in A s.t. (x,y)...

Both statements 1 and 2 are given as an explanation of why the original statement is true, but I don't understand why you can use statement 2 (since in the original vector equation you do not have Sin2(t), -Cos2(t)) Show why r(t) = <e-t, Sin(t), -Cos(t)> approaches a circle as t →∞. 1. As...

I see. I didn't. At catch that the expansions were different. I hate when I make careless errors. Thanks

I am asking my mentor for my class about this question, but unfortunately the answers I get from her often take forever and do not always clear things up for me, so I hope someone out there in Physics Forum has a good way of explaining this to me. Here goes... The question has some...

Homework Statement Mathematica's calculation of ∫0Log(2)Sin[(\pi/2)e2x]exdx = -FresnelS[1] + FresnelS[2] Remembering that FresnelS[x] = ∫0tSin[(\pi/2)t2]dt, You announce that a transformation you can use to help explain Mathematica's output is that every time x goes up by one unit, t=...

Thanks Sammy. I had never encoutered the Sinc Function before. After your hint, and a little help from google, I found that Sinc[x]= (Sin[x])/x. So xSinc[x] should be Sin[x], which makes the problem much easier. I think that should have been another hint given, I'm only working in Calc II ;).

nope. Still stuck

Wait, maybe I undertstand it. Do you have to use integration by parts method twice? i.e., letting u[x] = SinIntegral[x], and v^\[Prime][x] = 1; u^\[Prime][x] = Sinc[x] ; v[x] = x Which after applying the formula would get you to tSinIntegral[t] - ∫0tSinc[x]dx. Then you run the integration...

Homework Statement Calculate the following integral exactly (no approximations) by the method of integration by parts: ∫0t SinIntegral[x] dx Homework Equations the following hints are given: D[SinIntegral[x], x] = Sinc[x]; and SinIntegral[0] = 0 The Attempt at a Solution...

Okay I got it. Looking at it from that approach is a great way to see, conceptually, what is going on. Thanks for taking the time. Of course, it seems that using Taylor Serires could be a rather inefficient method. I'm sure we will be learning other methods as the class advances. Thanks again

The question asks the student to use Taylor's formula to calculate the exact values of higher derivatives f '[0], f '' [0], f ''' [0], ... , f^6'[0] of the function f[x] defined by the power series x/2 + x^2/12 + x^3/240 +x^4/10080 + ... +((k x^k)/(2 k)!) + ... My first...

Also didn't realize that you need two factorial symbols "!" rather than the usual one symbol for Mathematica to recognize and properly calculate the equation.