Midterm 1 Review Exercises True or False. In problems 1-4, justify your answer with an explanation or a counterexample. 1. A function has to be continuous at x = a if the limf (x) exists. 2. You can use the quotient rule to evaluate lim sin x 3. If there is a vertical asymptote at x = a for the function f(x), then fis undefined at the point x = a. 4. If limf (x) does not exist, then fis undefined at the point x = a. 5. Using the graph, find each limit or explain why the limit does not exist. a. lim f (x) *+-1 b. limf (x) x-1 C. lim f (x) x+0+ d. limf (x) x-+2 3 21 6. For the graph in problem 5, determine all x values where the function is discontinuous. Then determine if any of the discontinuities are jump discontinuities, removable discontinuities, or infinite discontinuities.In the following exercises, evaluate the limit algebraically or explain why the limit does not exist. 7. lim 2x3-3x-2 x-2 8. lim3x2 - 2x + 4 9. lim x3-2x3-1 3x-2 10. lim cot x 1 1. lim *+25 14-5 215 3x2-2x-8 12. lim 13. lim x2-1 t-1x3-1 14. lim x2-1 7-1 Vx-1 4-x 15. lim 7-4 Vx-2 16. lim J-41X-2 17. lim Javx3+1 Wal-1 18. lim cos( In problems 19 and 20, use the squeeze theorem to prove the limit. 19. limx cos (2nix) = 0 20. limx sin (#) = 0