Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Intermediate value theorem

  1. Apr 8, 2010 #1
    prove that the equation (1-x)Cosx=Sinx has at least one solution in (0,1)

    I am having some problem in proving that the equation is continous.

    Please help. Thank you
     
  2. jcsd
  3. Apr 8, 2010 #2

    mathman

    User Avatar
    Science Advisor

    1-x , cosx, sinx are all continuous, and you are not doing any dividing, so continuity is obvious.
     
  4. Apr 8, 2010 #3
    I realize it is continous. I just need prove that it is continous using the definition of continous

    for every ε > 0 there exists a δ > 0 such that for all x ∈ I,: |x-c|<δ⇒|f(x)-f(c)|<ε
     
  5. Apr 9, 2010 #4

    mathman

    User Avatar
    Science Advisor

    Can you assume each of the three terms are continuous or do need to first prove that? Once that is done, it is straightforward for whole expression since absolute value of each term is ≤ 1.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook