(a) nsider the change of variable from cartesian coordinates (x, y, z) to coordi- nates (r, y, 0) in R². X = exp(r) cos y cos 0, y = exp(r) sin 0, We will assume that y = [0, 2π) and 0 € [-π/2, π/2]. (i) Show that exp(r) = x² + y² + z²2. (ii) Compute the Jacobian of this transformation. I.e. find the determinant of the matrix z = exp(r) sin cos 0. ах ах ах др до до ду ду ду ar ap 20 əz əz əz or οφ οθ (iii) For € (0, π) and 0 € (-π/2, π/2), express r, y and in terms of x, y and z.

Find dy/dx without eliminating the parameter. A) tan(t) B) sin(t) (2n + 1)т x = 6 tan(t) – 2, y = 4 sec(t) + 3, t + 2 C) csc(t) D) sec(t)