Reset 76 Pre-Calculus Final Review #3 Name 2nd Semester 2018-2019 Period: Calculator Problems Note: Round all decimal values to three places. 1. A series is show below. Determine whether the series converges or diverges. If converges, find the sum. 7 7 6 24 96 384 2. A single cell amoeba doubles every 4 days. About how long will it take one amoeba to produce a population of 1000? 3. The temperature, in degrees F, of the water in a large fish tank is modeled by the function T(x) = In(1+x) +52.4, where x is the number of pebbles in the tank. Approximately how many pebbles are in the tank if the water is 58.3 F? 4. What is the value of lim- * - 92 x-3 x+3 5. When a = 25,000, what is the sum of the infinite sequence defined by the equation a, =0.8a _; nez, n>1 6. Healing of Wounds: The normal healing of wounds can be modeled by an exponential functions. If A represents the original area of the wound and if a equals the area of the wound after n days, then the formula A= Ae-035 , describe the area of a wond on the nth day following an injury when no infection is present to delay the healing. Suppose a wound initially had an area of 100 centimeters. (a) If healing is taking place, how large should the area of the wound be after 3 days? (b) How large should it be after 10 days? (c) How many days will it take before the wound is 11 square centimeters? 7. Solve: (a) 2log, x - log, (x-1) =1 (b) 41n(2x +3) =11Reset 779 Pre-Calculus Final Review #2 Name 2nd Semester 2018-2019 Period: Non-Calculator Problems Prove the following (two column proof required) 1. (csc x +1)(csc x-1) = csc x sin x COs X ci = csc x 3. 1+cot x_ = cot x cos* X 1-cos x sin x 1 + tan x 4. Solve. Give exact answer log(x-1) + log(x+1) = log8 Simplify the complex fraction x - 1+ - 2 x - 4 6. x+1 x x+3+ - 6 X x -4 x+1: 7. If tan O is undefined and OS OS 27 , what is 0? For 8 -9, find the exact value. 8. tan sec ? - cos 9. cot(-2) 10. Solve. 3sin x = 2 sin x +1 on the interval [0, 2x ) 1 1. Determine the quadrant in which O lies if cos 0 0. 12. If cos 0 = = and tan 0