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Calculus/how to prove does not exists linlit by definition of limit?

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Expert: Alon Mandes - 9/7/2008


Question
Let F(x)={0, if x is irrational
         2, if x is rational
Use definition of limit to prove that limit x->0 f(x) does not exists

Answer
The definition of limit is Lim x->a+ = Lim x->a- = Lim x->a.
Where a+ represent approaching a from the right & a- is approaching
a from the lift. In every approach we will reach infinite number of
irrational numbers as well as infinite number of rational numbers....
. . . .  0 . . . .
. . . .    . . . .
This is the visualizing image of the approach. So we can claime :
For every small x we choose we can show that
Lim x->0+ = 0 , Lim x->0- = 2
Hence, the limit for the function doesn't exist.

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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