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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 - ,

    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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