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Calculus/finding the slope.

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Expert: Alon Mandes - 5/26/2009


Question
Hello, my question is about this problem

Find the slope of the tangent line to the ellipse
(x^2/16)+(y^2/4)= 1 at the point (x,y)

I need to find the slope and the points where the slope is undefined..

How do I find this??

Answer
Slope of a curve f(x,y)=0 is defined as y'(x,y). To find y' we
perform implicit derivative on the equation curve :
(x^2/16)+(y^2/4)= 1
x/8+½yy'=0
y'(x,y)=-x/4y .
The slope is not defined at the point (0,0) & also not defined along the axis y=0 .

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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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

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

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