Recent content by Jaquis2345

  1. J

    Can a Function Have Two Different Tangent Lines at the Same Point?

    Proof: Suppose f is a function and x is in the domain of f s.t. there is a derivative at the point x and sppse. there are two tangent lines at the point (x,f(x)). Let t1 represent one of the tangent lines at (x,f(x)) and let t2 represent the other tangent line at (x,f(x)) s.t. the slopes of t1...
  2. J

    Bounded non-decreasing sequence is convergent

    After working on the problem for a while this is what I got (roughly). Since the point x is to the right of every point in the sequence, then from the completeness axiom there is either a rightmost point of the set contains all points of the sequence or a first point to the right of that set. I...
  3. J

    Bounded non-decreasing sequence is convergent

    After emailing my professor it seems there was a typo in the problem we were given. I just need to show that the sequence converges not that it converges to x.
  4. J

    Bounded non-decreasing sequence is convergent

    So far this is what I have. Proof: Let p1, p2, p3 be a non-decreasing sequence. Assume that not all points of the sequence p1,p2,p3,... are equal. If the sequence p1,p2,p3,... converges to x then for every open interval S containing x there is a positive integer N s.t. if n is a positive integer...
  5. J

    Prove: Limit Point of H ∪ K if p is Limit Point of H or K

    So no element of H can exist in the new interval other than possibly p. Thus, K exists in (a,b) and (c,d) where every point of K in that intersection is not equal to p. Right?
  6. J

    Prove: Limit Point of H ∪ K if p is Limit Point of H or K

    Summary: Definition: If M is a set and p is a point, then p is a limit point of M if every open interval containing p contains a point of M different from p. Prove: that if H and K are sets and p is a limit point of H ∪ K,then p is a limit point of H or p is a limit point of K In this proof I...
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