1,2

Problem 1. Let 6 and p be positive real numbers with 0

Problem 1. Let e and p be positive real numbers with 0 < e < 1. Let r(0) be the function ep/(l e cos(0)). For the curve with parametric equation (r(0) cos(0), r(0) sin(0)), find a formula for the slope of the tangent line at the point @(0), y(0)) as a fraction of simplified trigonometric equations in 0. Compute the two angles T/ 2 < 0 < T//2 at which the tan- gent line is horizontal, and compute the distance between the y-coordinates of these two points (the "major axis") as a simplified fraction in e and p. Problem 2. Let y f@) for the function f@) (e + ex) with domain (00, +00) and range (1, +1). Check that an inverse function is given by a; g(y), g(y) In((l + y)). Check using derivatives of logarithm functions that g/(y) equals 1/(1 y2). Next compute the derivative f'@) and use your formula to compute Check that this also simplifies to 1/(1 y2).