MA460 LIMITS NAME_____________________________ Instructions: Show your work neatly on a separate sheet of paper. 1. Let f (x) =x + 1 ! 2x ! 3if x " !1 and x # 3,k if x = 3.$%&'&. Find k so that the graph of ƒ is connected (i.e., ƒ is continuous.) 2. Let ƒ(x) = x31 – x2. Find (a) limx! "f (x) (b) limx!1"f (x) (c) limx!1+f (x) (d) limx! "1"f (x) (e) limx! "1+f (x) 3. (a) limx! "5x + 29x2+ 1 (b) limx! " #5x + 29x2+ 1 4. Let f (x) =x2+ 3x – 4x2– 6x + 5. Find (a) limx! "f (x) (b) limx!1+f (x) (c) limx!1"f (x) (d) limx! 5+f (x) (e) limx! 5"f (x) 5. limx!37"⎣2 + 7x ⎦ 6. limh!01x + h"1xh, x ≠ 0 7. limx! 2"| 7x – 14 |x2+ x – 6 8. limx! "x – 1x2+ 3 + x2+ 19. f (x) =!x2if x < 1,x3if x " 1.#$%Find limx!1f (x). (Note that limx!1f (x) doesn't exist.) 10. f (x) =!x2if x < 0,x3if x " 0.#$%Find limx! 0f (x) and limx! 0f (x). Can you state a theorem based on this problem and problem 9 ? 11. limt ! x 12t + 3"12x + 3t " x 12. limt !"/ 2sin t # 1t #"2 13. (a) limx! 0sin 7xtan11x (b) limx! 01 – cos