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Question
I need to know how to solve the following derivative:
lim sqrt(x-1)
h->0
So, you are interested in calculating the derivative of sqrt(x-1).
Ok, let's use the definition:
Lim [f(x+h)–f(x)]/h =
h->0
Lim [sqrt(x-1+h)-sqrt(x-1)]/h
h->0
Mutliply numerator and denominator by [sqrt(x-1+h)+sqrt(x-1)], expand, group like terms and simplify.
=Lim [sqrt(x-1+h)-sqrt(x-1)][sqrt(x-1+h)+sqrt(x-1)]
h->0 -----------------------------------------
h [(sqrt(x-1+h)+sqrt(x-1)]
=Lim (x-1+h-x+1)
h->0 --------------------------------
h[(sqrt(x-1+h)+sqrt(x-1)]
=Lim 1 / { sqrt(x-1+h)+sqrt(x-1) }
h->0
= 1/2sqrt(x-1)
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".
Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.
Education/Credentials
M.A in Mathematics & Bs.c in Electronics.
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