re: Differential Calculus

Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation.

x^2cos^2y - siny = 0

Note: I forgot the ^2 for cos on the previous question. Sorry.

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  1. x = 0, y = pi

    -x^2 2 cos y sin y dy +cos^2y 2 x dx - cos y dy = 0

    2 cos^2 y x dx=cosy (2x^2siny+1)dy

    dy/dx = slope m

    m = 2 x cos y/(2x^2siny+1)
    at (0,pi)
    m = 2 * 0 = 0 Oh my :) horizontal there
    so what is y at x = 0 and y = pi
    LOL, zero
    so along the x axis

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  2. I mean parallel to x axis and y = pi
    for part 2, normal is up the y axis
    see
    http://www.wolframalpha.com/widgets/view.jsp?id=91851988c40ebbe236f5561e167c9ab8

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  3. Just copy your function into there:
    x^2cos^2y - siny = 0

    look at the solution close to (0,0)

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