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Calculus/Limits and Polynomials

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Expert: Alon Mandes - 9/11/2008


Question
Find examples of polynomials p(x)and q (x) such that lim(x->infinity)
p(x) = infinity and lim(x->infinity) q(x) = infinity. AND

A. lim(x->0) [p(x) + q(x)] = 7
B. lim(x->0) [p(x)q(x)] = 10
C.  lim(x->infinity) [p(x) / q(x)] = infinity
D.  lim(x->infinity) [p(x) / q(x)] = 10


Answer
Ok, Kristin , we have the condition :
p,q->INF when x->INF that mean they are diverging functions.

lets start with A :
We know that p(x)=e^x->0 when x->0 & e^x->INF when x->INF.
we also know that q(x)=x->0 when x->0 .
So, we can claim that :
Lim(x->0) [7e^x + x] = 7

As for B :
We know that e^x/x->INF when x->INF so this will be p(x).
The function xcos(x) also goes to INF when x->INF because cos
is a bounded function. So,
Lim(x->0) [(10e^x)/x * xcos(x) ] = Lim(x->0) [(10e^x)*cos(x)] =10

As for c
let's take p(x)=e^x & q(x)=sqrt(x)

As for D :
we choose p(x)=10x & q(x)=x+1, so
Lim(x->INF) [10x/(x+1)] = 10

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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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