1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help finding the midpoint of a closed interval & more

  1. Sep 12, 2011 #1
    Hey everyone,

    This is a review of some stuff I learned in highschool, but I haven't actually done anything calculus related in about 2 years, and to be honest it looks foreign to me, if someone could help jog the old noodle it would help tremendously.

    The first question is as follows;

    1. There is a useful way of describing the points of the closed interval [a,b], as usual we assume that a<b.

    a)Consider the interval [0,b], for b>0. Prove that if x lies in [0,b], then we have x=tb for some t with 0≤t≤1. What is the significance of the number t? What is the midpoint of the interval [0,b]?

    b) Prove that if x ∈ [a,b], then we have x = (1-t)a+tb for some t with 0≤t≤1. What
    is the midpoint of the interval [a,b]? What is the point 1/3 of the way from a to b?

    c) Prove conversely that if 0≤t≤1 then (1-t)a+tb is in [a,b].



    I have given this problem much though, and even asked some engineer buddies but the answer seems to elude all of us, perhaps t=inverse of b and the significance of that is... something.

    I'm really grabbing at all I can get here, if anyone could help explain this to me I would appreciate it.

    Thanks so much
     
  2. jcsd
  3. Sep 12, 2011 #2

    Mark44

    Staff: Mentor

    t is just a number between 0 and 1 (inclusive). Try thinking about this with some concrete numbers. Suppose you're working with the interval [0, 1]. What's the midpoint of the interval?

    Now suppose you're working with the interval [0, 5]. What's the midpoint now?

    Can you make the leap to finding the midpoint of the interval [0, b]?
    Try this out with some specific numbers, say [3, 7]. Can you see why x = (1 - t)*3 + t*7 hits every point in [3, 7] for some value of t? If t = 0, which point in the interval do you get? If t = 1, what point do you get now?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help finding the midpoint of a closed interval & more
Loading...