1 As shown in the figure below, a camera is mounted on a point 30 m from the base of a rocket launching pad. The rocket rises vertically when launched, and the camera's angle is continually adjusted to follow the base of the rocket. a Express the height x as a function of the elevation angle . b Give the domain of the function in part a. c 2 Give the height of the rocket when the elevation angle is Consider the graphs of the functions a f and g shown in the figure below. Fill in the table below with the corresponding values of x 2 1 0 1 2 3 / 3. 4 f and g. 5 f ( x) g( x) a. Use the table in part a to evaluate each of the expressions listed below. Mathematics 265: Introduction to Calculus I (Rev. C13)Assignment 2 1 i. ii. iii. g o f (2) g o f (1) g o f (4) iv. v. vi. 3 f og(0) f og(4) f og(1) Indicate whether each of the limits listed below is well-defined. Explain your answer in each case. a lim x2 4 x 2 b x2 1 limcot x x3 1. Determine whether the evaluation of the limits given below are correct. If it is correct, explain why. If not, give the correct evaluation. a For lim x x we have , hence x 1 1/ x x x x x 2 3 3 x3 1 1/ x x2 x 3 lim lim 1 1/ x x x x x x Mathematics 265: Introduction to Calculus I (Rev. C13)Assignment 2 2 b lim x0 x2 sin( x / 2) x2 sin( x / 2)(1 cos(3x)) lim x 0 (1 cos(3x))(1 cos(3x)) 1 cos(3x) lim x0 x2 sin( x / 2)(1 cos(3x)) sin2 (3x) 2 x lim sin( x / 2)(1 cos(3x)) x 0 sin(3x) 2 x lim lim sin( x / 2) lim 1 cos(3x) x 0 sin(3x) x 0 x0 1 (1)(1) 9 1 9 Mathematics 265: Introduction to Calculus I (Rev. C13)Assignment 2 3