Calculus Problem





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Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: Calculus Problem
By Onizuka (Onizuka) on Thursday, October 02, 2003 - 10:08 pm: Edit

Was wondering if anyone could solve this problem and tell me step by step as to how they solved it. Any help would be greatly appreciated.

Consider the function
f(x)= {1 if x is a rational number
{0 if x is a irrational number

a) Show that the limit of f(x) as x approaches 'a' = Does not exist for all values
A E R, (where 'a' is an element of all real numbers incase you can't tell).

b) Draw an 'approximate' sketch of f(x) for
x E [0,1]

thanks

By Fairyofwind (Fairyofwind) on Thursday, October 02, 2003 - 10:10 pm: Edit

http://mathworld.wolfram.com/DirichletFunction.html


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