Recent content by toddlinsley79

  1. T

    Uniform Continuity of h(x)=x3+1 on [1, ∞)

    Ok so |f(x)-f(y)| = (x3+1)-(y3+1)=x3-y3 Now I'm confused about choosing my delta. I thought I was supposed to choose my delta as epsilon divided by (x3-y3) evaluated at x=1 and y=1 because the boundary is [1,infinity). However, this would lead to a contradiction because x3-y3=0 and I must...
  2. T

    Simple Proof of Weierstass Approximation Theorem?

    Homework Statement Let D={x in the set of real numbers: -3<x<3, x does not equal 0,1,2} and define g(x)=(cosx-1)/x + (x3-2x2-x+2)/(x2-3x+2) on D. Find G:R→R such that G is continuous everywhere and G(x)=g(x) when x is in set D. Homework Equations The Attempt at a Solution From a...
  3. T

    Polynomial Analysis: Show 2 Real Solutions for f(x)=0

    How can I find the value of x when I only know the signs of a0 and a4 and nothing about a2 and a3?
  4. T

    Polynomial Analysis: Show 2 Real Solutions for f(x)=0

    Well if a0>0, then in order for f(x) to be positive, a1x+a2x2+a3x3+a4x4<a0. What does this tell me about anything?
  5. T

    Uniform Continuity of h(x)=x3+1 on [1, ∞)

    Homework Statement Is h(x)=x3+1 uniformly continuous on the set [1,infinity)?The Attempt at a Solution Let \epsilon>0. For each x,y in the set [1,infinity) with |x-y|<\delta, we would have |(x3+1)-(y3+1)|=|x3-y3| Now how can I show that this is less than epsilon?
  6. T

    Polynomial Analysis: Show 2 Real Solutions for f(x)=0

    Homework Statement Let f(x)=a0+a1x+a2x2+a3x3+a4x4. Show that if a0a4<0, then f(x)=0 have at least 2 real solutions. Homework Equations The Attempt at a Solution Any hints? I can't tell how to begin an attempt for a solution.
Back
Top