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  1. H

    Finding all tangent lines through a point

    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...
  2. H

    Position on the plane of a man

    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...
  3. H

    Schools Odd academic situation and graduate school admissions

    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...
  4. H

    Fourier series convergence - holder continuity and differentiability

    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...
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    Countability subset of the reals proof

    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.
  6. H

    Intervals and their subsets proof

    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?
  7. H

    Topology intervals on the real line proof

    Homework Statement a) Let I be a subset of the real line. Prove I is an interval if and only if it contains each point between any two of its points. b) Let Ia be a collection of intervals on the real line such that the intersection of the collection is nonempty. Show the union of the...
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    Differential geoemtry tangent lines parallel proof

    Homework Statement Prove that a(s) is a straight line if and only if its tangent lines are all parallel. Homework Equations Frenet serret theorem The Attempt at a Solution I'm confused on the direction "if the tangent lines are parallel then a(s) is a straight line". Assume all the...
  9. H

    Diameter of a set

    Homework Statement Define diam(X) of a set X, X a nonempty subset of arbitrary metric space, as diamX=supremum{distancefunction(x,y):x,y in X}. Let K be the two cell formed by two points a=(2,3) and b=(4,6) in the xy plane. Find diameter of K and show this is the diameter. Homework...