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2.3 Exercises 1. Given that (e) lim [x2f (x) ] (f) f(- 1) + lim g(x) - 2 lim f(x) = 4 lim g(x) = -2 lim h(x) = 0 - 2 *-+ 2 find the limits that exist. If the limit does not exist, explain y = f(x) y = g(x) why. * - 2 (a) lim [f (x) + 5g(x)] (b) lim [g(x)]3 (c) lim of(x) (d) lim 3f (x) 2- 2 x-2 g(x) 3-9 Evaluate the limit and justify each step by indicating the g(x) g (x) h(x) appropriate Limit Law(s). (e) lim 1-2 h(x ) - 2 f ( x ) 3. lim (4x2 - 5x) 4. lim (2x3 + 6x2 - 9) 2. The graphs of f and g are given. Use them to evaluate each 5. lim (v2 + 20) (203 - 5) 3+2 + 1 0 - 2 6. lim limit, if it exists. If the limit does not exist, explain why. 1-7 + 2 - 5+ + 2 (a) lim [f(x) + g(x)] (b) lim [f (x) - g(x)] 7. lim V9 - u3 + 2u2 4 - - 2 8. lim Vx + 5 (2x2 - 3x) x -+ 3 21 5 - 1 4 ) 3 9. lim (c) lim [f(x)g(x)] (d) lim f( x) 1 - - 1 5+2 + 4 1 -+ 3 g(x)10. (a) What is wrong with the following equation? x2 + x - 6 x - 2 =x+3 (b) In view of part (a), explain why the equation x2 + x- 6 lim x - 2 X - 2 lim (x + 3) x-2 is correct. 11-34 Evaluate the limit, if it exists. 11. lim (3x - 7) 12. lim (8 - 5x) x - 6 12 - 21 - 8 13. lim x'+ 3x 1 - 4 14. lim 1 -4 x ->- 3 x2 - x - 12 x2 + 5x + 4 15. lim x' + 3x 16. lim r -x 2 x - 2 X-4 x - x - 12 2 - X - 6 2x2 + 9x -5 17. lim 18. lim x->-2 3x2 + 5x - 2 * - - 5 x - 25 3 - 27 u +1 19. lim 20. lim 1 - 3 12 - 9 16- - 1 4 + 1 (h - 3)2 - 9 9 -X 21. lim 22. lim h x-09 3 - Vx 19 + h - 3 2 - x 23. lim 24. lim h - 0 h Vx + 2 - 2 X 3 (-2 + h) -+2-1 25. lim 26. lim *-3 x - 3 h - 0 h 1+t- v1-t 27. lim 28. lim 1-0 1-+ 0 x2 - 4x + 4 4 29. lim 30. lim x- 16 16x -xz x-$2 x4- 312- 4 Vxz + 9-5 31. lim 32. lim x - -4 x+ 4 1-20 ( x + h )2 ( x + h ) 3 - x3 33. lim 34. lim h - 0 h h -0 h