MATH 135 -- Calculus 1 

 

Problem 40 from section 1.7 in the text asked for a derivation  

of the coordinate functions for the parametric curve called 

the "witch of Agnesi."   Here is an animated plot illustrating 

the definition of that curve, with a = 1; -1 

 

with(plots); -1; Circle := plot([cos(t), `+`(sin(t), 1), t = 0 .. `+`(`*`(2, `*`(Pi)))], color = red); -1 

HorizontalLine := plot([t, 2, t = 0 .. 10], color = red); -1; RotatingLine := animate(plot, [`*`(tan(theta), `*`(x)), x = 0 .. `+`(`*`(2, `*`(cot(theta))), 0.1e-1)], theta = .2 .. `+`(`*`(`/`(1, 2), `...
HorizontalLine := plot([t, 2, t = 0 .. 10], color = red); -1; RotatingLine := animate(plot, [`*`(tan(theta), `*`(x)), x = 0 .. `+`(`*`(2, `*`(cot(theta))), 0.1e-1)], theta = .2 .. `+`(`*`(`/`(1, 2), `...
HorizontalLine := plot([t, 2, t = 0 .. 10], color = red); -1; RotatingLine := animate(plot, [`*`(tan(theta), `*`(x)), x = 0 .. `+`(`*`(2, `*`(cot(theta))), 0.1e-1)], theta = .2 .. `+`(`*`(`/`(1, 2), `...
HorizontalLine := plot([t, 2, t = 0 .. 10], color = red); -1; RotatingLine := animate(plot, [`*`(tan(theta), `*`(x)), x = 0 .. `+`(`*`(2, `*`(cot(theta))), 0.1e-1)], theta = .2 .. `+`(`*`(`/`(1, 2), `...
HorizontalLine := plot([t, 2, t = 0 .. 10], color = red); -1; RotatingLine := animate(plot, [`*`(tan(theta), `*`(x)), x = 0 .. `+`(`*`(2, `*`(cot(theta))), 0.1e-1)], theta = .2 .. `+`(`*`(`/`(1, 2), `...
HorizontalLine := plot([t, 2, t = 0 .. 10], color = red); -1; RotatingLine := animate(plot, [`*`(tan(theta), `*`(x)), x = 0 .. `+`(`*`(2, `*`(cot(theta))), 0.1e-1)], theta = .2 .. `+`(`*`(`/`(1, 2), `... 

display(Circle, HorizontalLine, RotatingLine, TriangleHoriz, TriangleVert, Witch, scaling = constrained); 1 

Plot_2d