Recent content by hlin818

Homework Statement Find all tangent lines of the graph f(x)=x+3/x that have a y intercept of 4. Homework Equations The Attempt at a Solution Assume a is the x coordinate of a point of tangency. Thus the point of tangency is (a, a+3/a). We know the tangent line must pass...

Bah. Never mind, I was looking at something wrong. So would the set of all n=infinity locations be the whole argand plane? It seems that varying values the angle theta and the step function could eventually allow the sum of values to "converge" to any point on the plane.

Thank you guys, that takes care of the angle problem. So would the general nth position be Zn=1*e^(i0)+f*e^(i*theta)+...+f^n*e^(n*i*theta)? Somehow I doubt this is correct - shouldn't the radius continually be decreasing?Oops - I meant to the *horizontal*. After the initial step theta goes...

Homework Statement An man starts on 0+0i of the complex plane. During the first walk step he moves a distance 1 to the right and lands on 1+0i. At each walk phase after this initial one the walk length decreases by a factor f<1 and he changes direction by an angle theta (measured from the...

Thank you to both of you, that is reassuring to hear. I'll be sure to apply to programs outside the top ten. To be honest there are a lot of schools I would want to go to outside of the prestigious ones but from the research I've done it seems that obtaining a teaching position in academia...

How well prepared were you for the exam? Did you know the material inside and out? I'm *not* saying this is parallel to your situation but something I used to regard as exam nerves was, at the crux of it, a lack of proper preparation. I studied, sure, but I didn't sufficiently prepare enough...

To elaborate on said situation - I went to a top 50 US public university for a few years majoring in math and during this period of time I had no significant interest or motivation in school, much less any graduate school aspirations. I didn't do *horrible*, but my gpa was about a 3.1. I took...

final bump

Sorry about the bump, but this question is killing me. I don't feel like the book explained this convergence criteria well at all.

I may be wrong about the holder condition, but it looks to me like f(x) is holder continuous as long as the exponent in the condition is equal to or less than 1/2.

Homework Statement Given each of the functions f below, describe the set of points at which the Fourier series converges to f. b) f(x) = abs(sqrt(x)) for x on [-pi, pi] with f(x+2pi)=f(x) Homework Equations Theorem: If f(x) is absolutely integrable, then its Fourier series converges to f...

If we do this by contradiction wouldn't the negation be to assume that X and Y do not have cardinality equal to (a,b)?

Homework Statement Let (a,b)=XUY, X,Y arbitrary sets where (a,b) is an arbitrary interval. Prove that either X or Y has the same cardinality as that of (a,b). Homework Equations The Attempt at a Solution Really lost.

Ah completely overlooked that, thanks. I'll post up the full problem because now I'm sort of stuck.

Homework Statement I reduced another problem to the following problem: If I is an interval and A is a subset of I, then A is either an interval, a set of discreet points, a union of the two. Homework Equations The Attempt at a Solution Is this trivial?