1. Sep 20, 2012 #1

   maiad

   

   1. The problem statement, all variables and given/known data
   Let f be the function such that f(x)=1+^2 if x is irrational and f(x)=1+4x^4 if x is rational.
   
   Use the Squeeze Theorem to find (lim x->0)f(x).
   Clearly, for all real numbers x, f(x)>=1. Next, we note that for a real number x,
   
   x^2−4x^4=(x^2)(1−4x^2)>=0
   if and only if ? >=0. This means that x^2>=4x^4 if and only if x [?,?]
   
   3. The attempt at a solution
   I've been stuck on this question for a while.any hints to start me off?

    

   maiad, Sep 20, 2012
2. 
   Phys.org - latest science and technology news stories on Phys.org

   • • Game over? Computer beats human champ in ancient Chinese game
   • • Simplifying solar cells with a new mix of materials
   • • Imaged 'jets' reveal cerium's post-shock inner strength
3. Sep 20, 2012 #2

   HallsofIvy

   

   Staff Emeritus

   Science Advisor

   If [itex]x_n[/itex] is a sequence of rational numbers, converging to 0, what is [itex]f(x_n)[/itex] for all n? What is the limit as n goes to infinity?
   
   If [itex]x_n[/itex] is a sequence of irrational numbers, converging to 0, what is [itex]f(x_n)[/itex] for all n? What is the limit as n goes to infinity?

    

   HallsofIvy, Sep 20, 2012

• Log in with Facebook
• Log in with Twitter

Your name or email address:

Do you already have an account?

• No, create an account now.
• Yes, my password is:
• Forgot your password?

Stay logged in