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Johathan Wehner

Feb 20, 2025

Consider the relation defined by the equation tan(y)= x + y for x in the open interval -2 pi < x < 2 pi?

a. Find dy/dx in terms of yb. Find the x and y coordinate of each point where the tangent line to the graph is verticalc. Find d^2y/dx^2 in terms of y
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Alycia Zemlak

Feb 20, 2025

a.Implicit differentiation:sec²y (dy/dx) = 1 + dy/dx(sec²y - 1)(dy/dx) = 1tan²y (dy/dx) = 1dy/dx = 1/tan²ydy/dx = cot²yb.dy/dx is undefined at y = nπ, where n is an integer.tan(nπ) = x + nπ 0 = x + nπx = -nπSolutions satisfying -2π < x < 2π:(-π, π), (0, 0), (π, -π)c.dy/dx = cot²yd²y/dx² = 2cot(y)(csc²y)(dy/dx)d²y/dx² = 2cot(y)(csc²y)(cot²y)d²y/dx² = 2cot³y csc²y... Show More
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