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Expert: Alon Mandes - 9/1/2009


Question
I'm having trouble evaluating the difference quotient for the given function and simply that answer, the question is

f(x)=x3, f(a+h)-(f(a)
---------------------
        h

Thanks again

Answer
f(x)=x³ , Let's differentiate  : f'(x) at x=a .
Lim  [ f(a+h)-(f(a) ] / h  =
h->0
Lim  [ (a+h)³-a³ ] / h  =
h->0
Lim  [ a³+3a²h+3ah²+h³-a³ ] / h  =
h->0
Lim  [ 3a²h+3ah²+h³ ] / h  =
h->0
Lim  [ 3a²+3ah+h² ]h / h  =
h->0
Lim  [ 3a²+3ah+h² ]   =  3a²+3a*0+0² = 3a² .
h->0

Alon.  

Calculus

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Alon Mandes

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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 .

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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.

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M.A in Mathematics & Bs.c in Electronics.

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