1. Let C be the curve parametrizationt, sect), -;

1. Let C be the curve parametrized by c(t) (tan t, sect) (a) Find dy/d:r. (b) Find an equation of the tangent line when t = 7r/4. dy (c) Find lim and lim dx t.r/2- d'.r (d) Sketch the curve C along with the lines y = and y = lim t.,r/'2- do: M c, where lim = m and (e) Find a Cartesian equation of the parametric curve. Does this match what you see in the sketch from part Explain. (f) Set up two integrals for computing the area between the curve and the axis for 0 t } , one using the parametric setup and one using the Cartesian equation of the curve. Use a trigonometric substition on the Cartesian integral to verify that these two integrals are the same.