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Calculus/last part of my homework, PLEASE HELP!

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Expert: Alon Mandes - 11/24/2008


Question
A particle moves in the plane along a curve C with representation. r(t)=tcos(t)i+tsin(t)j for t≥0

(the i and j have a hat over them)

Find the curvature of C at the point corresponding to t=pi/2


I cannot figure out this question for the life of me, can you please help????


Answer
C=|x'(t)y''(t)-x''(t)y'(t)|/[(x'(t)^2+y'(t)^2]^(3/2). In our case
x(t)=tcos(t) & y(t)=tsin(t).
So, let's get to work :
x'(t)=cos(t)-tsin(t)
x''(t)=-sin(t)-tcos(t)-sin(t)=-2sin(t)-tcos(t)
y'(t)=sin(t)+tcos(t)
y''(t)=cos(t)+cos(t)-tsin(t)=2cos(t)-tsin(t)

Now, you can continue from here.

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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