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Calculus/limits and rationalizing
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Question
hi! can you help me with this problem?
If h(x)=(squareroot of x+9) + 3/ x....
Show the lim h(x) does exist as x approaches 0 and find the limit..
If I understood correctly , then
√(x+9) + 3
h(x) = ---------------
x
We can't plug 0 into the function because it will jump to ∞.
Instead we will perform a trick :
We know that [√a - b][√a + b]=a-b^2. & we also know that
M M A
- = ------- * -------
N N A
So,
√(x+9) + 3 [√(x+9) + 3][√(x+9) - 3]
---------------- = ---------------------------
x x [√(x+9) - 3]
x+9-3^2
= ---------------------
x [√(x+9) - 3]
x
= -------------------
x [√(x+9) - 3]
1
= --------------- = h(x)
[√(x+9) - 3]
& still if we plug 0 into the function after the trick, it still
jumps to ∞. So, our conclusion that this function is not continues
in point x=0.
& Still, if you meant h(x)=√(x+9)+(3/x) , still this function jumps
to ∞ in x=0. It's a point with singularity.
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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