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Question
For what value of m and b is the statement:
lim [sqrt(mx+b)-3]/x=1?
x->0
Thank you!
√(mx+b) - 3 [ √(mx+b) - 3 ] [ √(mx+b) + 3 ]
------------ = ---------------------------------------- =
x x[ √(mx+b) + 3 ]
mx+b-9 mx b-9
---------------- = ------------------ + --------------
x[ √(mx+b) + 3 ] x[ √(mx+b) + 3 ] x[ √(mx+b) + 3 ]
1st of all b must be equal 9 , thus the second term will be zero.
hence,
Lim mx m
x->0 ----------------- = ---------------
x[ √(mx+b) + 3 ] √b + 3
We are interested in the case where the limit converge to 1 . Thus,
m
------- = 1
√b + 3
m
------- = 1
√9 + 3
Hence, m=6 .
So the answer will be : m=6,b=9 .
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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