Recent content by brooklysuse

  1. B

    MHB Proving a limit to infinity using epsilon-delta

    Looking to use this definition. f:A->R, A is a subset of R, (a, infinity) is a subset of A. lim f(x) =infinity if for any d in R, there exists a k>a such that when x>k, then f(x)>d. x->infinity
  2. B

    MHB TFAE proof involving limit and convergent sequence

    Let A ⊆ R, let f : A → R, and suppose that (a,∞) ⊆ A for some a ∈ R. Then the following statements are equivalent: i) limx→∞ f(x) = L ii) For every sequence (xn) in A ∩ (a,∞) such that lim(xn) = ∞, the sequence (f(xn)) converges to L. Not even sure how to begin this one, other than the fact...
  3. B

    MHB Proving a limit to infinity using epsilon-delta

    lim 2x + 3 = ∞. x→∞ Pretty intuitive when considering the graph of the function. But how would I show this using the epsilon-delta definition?Thanks!
  4. B

    MHB Finding Cluster Points/Accumulation Points

    Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}. Justify your answer with proof. I believe 0 is a cluster point but I can't figure out how to prove this, or how to prove any other point is not. Any quick help would be appreciated. Thanks.