Mathematics 31 Online Unit 1B Assignment: Limits - x 2 h. lim- fix-1 2 Vx - 1 i. lim - x - 1 ADLC | Alberta Distance Learning Centre 71. Use the graph of y =f(:c), shown below. to answer the following questions. ADLC I Alberta Dislance Learning Centre 1 Unit: 1 B Assignment: Limits Malhsmatics 31 Online (9 a. Complete the chart. iv. vi. vii. viii. ix. xi. xii. 4 4 a. Sketch the graph of y = f(x). 3 b. Determine the following limits, if they exist. lim f(x) x-0 ii. lim f(x) iii. limf(x) iv. lim f(x) x -+ 4 v. lim f(x) vi. limf(x) x +4" ADLC | Alberta Distance Learning Centre WMathematics 31 Online Unit 18 Assignment: Limits 12. Find the values of x for which the infinite geometric series (x - 2)1 + (x - 2): + (x 2)' + is convergent. 13. The second term in an infinite geometric series is :}z- and the third term is 3. Is it possible to determine the sum of this series? Explain. 2 ADLC | Alberta Distance Learning Centre 15 Unit 1B Assignment: Limits Mathematics 31 Online (1 -x) -1 2 j. lim X 4) 5. Show lim(x' - 2x) = (limx) - lim 2x * - 2 Left Side Right Side Left Side = Right Side 6. Using limit theorems, evaluate the following limits, where limf(x) = 1, limg(x) = 4, and limh (x) =- 2. Show all work. x -a 2 a. lim (f(x) 8 (x) ) x -a\\ h(x) ADLC | Alberta Distance Learning CentreUnit 1B Assignment: Limits Mathematics 31 Online 2 10. A pendulum on its first swing traces out a path 50 cm in length. On each successive swing, it traces out a path that is 90% as long. The total distance swept out by the swings of the pendulum forms an infinite geometric series. Determine the total distance the pendulum travels before coming to rest. 2 11. Find the sum of the infinite geometric 1 + (x+ 1) + (x+ 1) + (x+ 1)'+ ... if|x+ 1/ - 4 a. lim f(x) x- -4+ b. lim f(x) c. lim f(x) ADLC | Alberta Distance Learning Centre