18. 19. 20. 21. 22. 23. 24. Car A is travelling west at 50 mi/ h and car B is travelling north at 60 mi / h. Both are headed for the intersection of the two roads. At what rate are the cars approaching each other when car A is 0.3 mi and car B is 0.4 mi from the intersection? Answer: 78 mi/h. A kite 100ft above the ground moves horizontally at a speed of 8 ft / 5. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? Answer: 0.02 rad/s A rectangular storage container with an Open t0p is to have a volume of 10m3. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container. Answer: $163.54 Find the most general antiderivative of f (z) = 2 + 6cos :1: Answer: 3323/2 + 66inz + 0 Let A be the area of the region that lies under the graph of f (3:) = 2:1:2 + 5 between 3 = 0 and a: = 4. Using right endpoints nd expressions for A as a limit. Evaluate 188 the limit without using the Fundamental Theorem of Calculus. Answer: T Let A be the area of the region that lies under the graph of f(9:) = 5:133 3:1: between a: = 0 and a: = 3. Find an expression for the area A as a limit. Evaluate the limit 351 without using the Fundamental Theorem of Calculus. Answer: T Curve sketching: For each of the functions (i) f(a:) = 334 2.1:2 + 3 (ii) f(:1:) = 35/3 5532/3 (iii) f(a:) = answer the following questions. (a) State the domain of f. (b) Find the a: and y intercepts. (c) Does f have even symmetry, odd symmetry, or neither? (d) Determine the vertical asymptote(s) of the curve 3; = f (11:) (if any), and deter- mine the left and right limits at each of these asymptotes. (e) Determine the horizontal asymptote(s) of the curve y = f (:r) (if any). (f) Find the intervals of increase/decrease of f. (g) Find local maximum and local minimum values of f, if any. (h) Find the intervals of concavity. (i) Determine the inection point(s), if any. (j) Sketch the graph y = f (3:) using above information. 23341 (93+1l2