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Math 106 – Graded HW (Test 2 - #3) Name _____________________________ Refer to the graph to find all x-values where: 1. an infinite discontinuity occurs. __________ 2. a jump discontinuity occurs. ___________ 3. a removable discontinuity occurs. _________ 4. Is 𝑓(𝑥) continuous at 𝑥 = 3? _______ at 𝑥 = 4? _______ 5. Is 𝑓(𝑥) left-continuous at 𝑥 = −4?_____ at 𝑥 = 1?_____ at 𝑥 = 4?_____ at 𝑥 = 6?______ 6. Is 𝑓(𝑥) right-continuous at 𝑥 = 5? _______ at 𝑥 = 1?_______ at 𝑥 = 6? ________ 7. Is f(𝑥) continuous over the interval [0,2]?_______ [2,3]? _________ (−∞,−5]? ________

CONTINUITY

8. Find all x values where the function is discontinuous (i.e. where the function is undefined):

a) 𝑓(𝑥) = 56 768969:

b) 𝑓(𝑥) = 6 8;<6;= 76>9=?6

c) 𝑓(𝑥) = 695 68;75

d) 𝑓(𝑥) = @69: @69:

9. Let 𝑓(𝑥) = A 5𝑥 + 2 𝑖𝑓 𝑥 < −1 𝑥7 − 4 𝑖𝑓 − 1 ≤ 𝑥 < 2 −3𝑥 + 1 𝑖𝑓 𝑥 ≥ 2

Use the Definition of Continuous to determine if 𝑓(𝑥) is continuous at: a) 𝑥 = −1 b) 𝑥 = 2

c) Use the Definition of left-continuous to determine if 𝑓(𝑥) is left-continuous at 𝑥 = −1.

10. Find the value of c that makes 𝑓(𝑥) = G 𝑥 7 + 𝑐 𝑖𝑓 𝑥 < −2

−4𝑥 + 9𝑐 𝑖𝑓 𝑥 ≥ −2 continuous.

LIMITS Find the limit:

11. lim 6→=

=9√6 69=

12. lim 6→<

6896 689=O

13. lim 6→P

Q R9

Q (ST8)8

6

14. lim

6→<

69< √68;U95

15. lim

6→5

:69=5 =PP9<68

16. lim 6→7

569=P <689569O

17. lim

6→7 V < <968

− = 796

W

18. lim 6→P

√=:;69=: 6

19. lim 6→U

=?X√69OY 69=7

20. lim 6→97

6>;? 689O69=O