MATH 142, Calculus Show all work neatly, clearly and carefully

MATH 142, Calculus Show all work neatly, clearly and carefully. Calculators are not allowed in the exam. • Scan your Solution and upload it as a single pdf file on the blackboard. • You cannot use your textbook, class notes, internet. Quizzes are an individual work. • You can refer to the Basic Integration Formulae in Section 8.1. 1. (20 pts) Find a Cartesian Equation for the parametric equation x = 3 − 3t, y = 2t, 0 ≤ t ≤ 1. Graph the cartesian equation. Indicate the portion of the graph traced by the parametric equations. 2. (25 pts) Find an equation of the line tangent to the curve x = 4 sin (t), y = 2 cos (t) at the point t = π4 . 1 3. (25 pts) Compute dy dx and d2 y dx2 for the parametric equations: x = 7t2 − 9t, y = t6 + 2t2 . 4. (25 pts) Find the arc length of the curve given by the parametric equations: x = sin (2t), y = cos (2t) where 0 ≤ t ≤ 2π. 5. (5 pts) Answer the following questions. Whatever you write will not be used against you, so please be honest. (a) What is one thing you liked about this class? (b) What is one thing you did not like about this class? 2