Posted by Anonymous on Sunday, February 27, 2011 at 11:38pm.
consider a point on a circle x2+y2=1.At what rate Y is changing with respect to X when the point is at X=1/2....

calculus  drwls, Monday, February 28, 2011 at 4:06am
There are two points on the circle with x = 1/2:
(1/2, sqrt3/2) and (1/2,sqrt3/2)
Which one are you talking about?
Anyway, what you want is dy/dx.
Use a ^ sign before exponents.
x^2 + y^2 = 1
Use implicit differentiation.
2x + 2y*dy/dx = 0
dy/dx = x/y = 1/sqrt3 or 1/sqrt3
depending upon which of the two points you are talking about.
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