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Calculus/Rate of Change

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Expert: Alon Mandes - 12/7/2008


Question
A spherical balloon is being inflated. Its radius in centimeters after t minutes is given by r(t)= 3 (t+6)^1/3, where 0<t<9. Estimate the rate of change of r with respect to t at t=6.
I have been trying to use f(a+h)- f(a)/ h but I don't think that's the right formula. My brain is fried....
Thank you for your help,
Kerstin

Answer
The form [f(x+h)- f(h)]/h is good when you are requested to
calculate rate of change from x1 to x2. But when you are requested
to calculate instant rate of change at a given point , you need
to derive the function. r'(t)=(t+6)^(-2/3) -> r'(6)=0.190

Now, if you are asked to find the rate of change from t1=0 to t2=6,
then you must use the definition of rate of change :
[f(t+h)- f(h)]/h. where h=0 & t=6.

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

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