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...
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...
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...
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...
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.
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?
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...
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...
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...