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Calculus/Discontinuity
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Question
Determine where the function g(x) has discontinuity. Label the type of discontinuity and if possible, write a new continous function.
g(x) = 2- 2cos(x)
----------
2x
If you set the value x=0 in the function you will get 0/0 which is
unknown, so we have singularity in this point. This singularity
point can lead to discontinuity. But first let's calculate the limit
of this function when x reaches zero :
Lim(x->0) [2-2cosx]/2x = Lim(x->0) [0-(-2sinx)]/2 =
Lim(x->0) sinx = 0. That means the limit is final & well defined.
// Note that I used the law of Ho'pital to calculate the limit //
We may define the function g(x) as follow :
g(x)=(2-2cosx)/2x for every x except 0
g(x)= 0 if x=0.
ALon.
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Answers by Expert:
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".
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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.
Education/Credentials
M.A in Mathematics & Bs.c in Electronics.
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