NAME : MATH 1151 AUTUMN 2017 WRITTEN HOMEWORK 2 INSTRUCTIONS : Calculators are permitted EXCEPT those calculators that have symbolic algebra or calculus capabilities. SHOW ALL WORK ! Incorrect answers with work shown may receive partial credit, but unsubstantiated answers will receive NO credit. MSLC tutors are not allowed to help you with this assignment. Due date : Tuesday, October 10, 2017, Recitation Class #1 ( 3 pts ) A light is at the top of a pole 80 ft high. A ball is dropped from the same height from a point 20 ft away from the light. Find how fast the shadow of the ball is moving along the ground 2 seconds later. Assume that the ball falls s = 16 t 2 feet in t seconds. Make sure to label the figure ! 2 WH2 AU17.nb #2 (3 pts) A figure below shows a part of the curve given by the equation sin (xy ) - x = 0. (a) Use implicit differentiation to find (b) Check (algebraically) that the point dy dx . 1 , lies on the curve. 2 3 (c) Use the result in the part (a) to find the slope of the line tangent to the curve at the point 1 , . 2 3 (d ) In the figure above draw the line tangent to the curve at the point Determine an equation of this tangent line. 1 , . 2 3 WH2 AU17.nb (e) Solve the equation sin (xy ) - x = 0 for y in terms of x, where 0 < x < 1, and obtain an expression y = f (x ), so that the point 1 , lies on the graph of the function f . 2 3 Calculate f ' (x ). Compare f ' (x ) with dy dx in part (a) and comment. 3 4 WH2 AU17.nb (f ) Let A be a point on the graph of the equation whose x - coordinate is 1 2 sin (xy ) - x = 0 (see figure below). Find the exact value of its y - coordinate. (g) Solve the equation sin (xy ) - x = 0 for y in terms of x, where 0 < x < 1, and obtain an expression y = g (x ), so that the point A lies on the graph of the function g. Calculate g ' (x ). Compare g ' (x ) with dy dx in part (a) and comment