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Expert: Alon Mandes - 9/5/2008


Question
How do I evaluate these problems?

(a) lim x->3 ln(3-x)
(b) lim x->4+ ln(x-3)

Answer
Hello Jessica, we are going to solve this kind of question in a
little bit different way. Now, we all know that if I plug 3 in the
Ln, I will get Ln(0), wich is -∞, but the issue here is to show the
way we approch the -infinity. & for that we will use the definition
of Limits : Lim f(x) = -∞ { when x->0 } mean, for every €>0 (very
small) exist M>0 (very big) so that if a<€ then f(a)<-M.
In our case we will convert  lim x->3 ln(3-x) by lim x->o ln(x).
Which is the same of course.
TO do so, let's take €<0.001 or €<1/1000.
Then Ln(1/1000)=Ln(1)-Ln(1000)=0-6.9.
So,in symbol way : if we take €=1/M (M very very big), then the Ln function will be 0-Ln(M)=-M' , which M' is very very big.
Hence , the  € that I will take will be 1/e^M'. This is my resolution
of approach to the -infinity.

I will leave the 2nd part (b) to you as an exercise. Follow the
same way.

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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