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$2.00 Uniformly Continuous

  • From Mathematics: Calculus
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  • Due on Apr. 30, 2008
  • Asked on Apr 28, 2008 at 9:38:14PM
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Def: a function f:D--->R is uniformly continuous on a set E in D in R iff for any given epsilon > 0 there exists delta such that |f(x)-f(t)|< epsilon for all x, t in E satisfying |x-t|< delta.

Using the def, determine whether or not the given functions are uniformly continuous

a)f(x)=x^3 with x in [0,2)
b)f(x)=x/x+4 with x in [0,2)
 


   
   
   
   
 
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cxxliu
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$2.00 uniformly continuous

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  • Posted on Apr 30, 2008 at 5:53:25PM
A:
Preview: ... + 3xd^2 + d^3.<br>We want this difference to be less than epsilon. Since x is less than 2, the above difference is less than<br>3(2^2)d + 3(2)d^2 + d^3 = 12d + 6d^2 + d^3. If we further restrict that d < 1, then d^3 < d^2 < d. So the above difference is less than 12 d ...

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