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Day 31 1. Limits - Exercises
True or False:




                         !     f (3) = 7

             DNE          !    f (3)   Undefined
Day 31 1. Limits - Exercises
True or False:




                           !   f (3) = 7
                   False
             DNE           !   f (3)   Undefined
Day 31 1. Limits - Exercises
True or False:




                               !   f (3) = 7
                   False   False
             DNE               !   f (3)   Undefined
Day 31 1. Limits - Exercises
True or False:




                               !   f (3) = 7
                   False   False            False
             DNE               !   f (3) Undefined
Day 31 1. Limits - Exercises
True or False:




                               !   f (3) = 7
                   False   False            False
             DNE               !   f (3) Undefined
                   True
Day 31 1. Limits - Exercises
True or False:




                               !   f (3) = 7
                   False   False            False
             DNE               !   f (3) Undefined
                   True    False
Day 31 1. Limits - Exercises
True or False:




                               !   f (3) = 7
                   False   False            False
             DNE               !   f (3) Undefined
                   True    False           True
1. Limits - Exercises
True or False:




                        !   f (0) = 5

             DNE            f (3)   Undefined
1. Limits - Exercises
True or False:




                           !   f (0) = 5
                   False
             DNE               f (3)   Undefined
1. Limits - Exercises
True or False:




                              !    f (0) = 5
                   False   False
             DNE                   f (3)   Undefined
1. Limits - Exercises
True or False:




                              !    f (0) = 5
                   False   False            True
             DNE                   f (3) Undefined
1. Limits - Exercises
True or False:




                              !    f (0) = 5
                   False   False            True
             DNE                   f (3) Undefined
                   True
1. Limits - Exercises
True or False:




                              !    f (0) = 5
                   False   False            True
             DNE                   f (3) Undefined
                   True    True
1. Limits - Exercises
True or False:




                              !    f (0) = 5
                   False   False            True
             DNE                   f (3) Undefined
                   True    True            False
2. Notes
Find the following limit
                           2
                   lim 2x − 3x − 4
                   x→−1
2. Notes
Find the following limit
                           2
                   lim 2x − 3x − 4
                   x→−1
3. Exercises
Find the following limits

1. lim x
      1
   x→− 3

2. lim π
   x→−1

        3x + 7
3. lim
   x→4 x + 1

         x + 15
4. lim
   x→4     3
          5− x
5. lim
   x→−6    2
3. Exercises
Find the following limits

1. lim x
      1
   x→− 3
                            -1/3

2. lim π
   x→−1

        3x + 7
3. lim
   x→4 x + 1

         x + 15
4. lim
   x→4     3
          5− x
5. lim
   x→−6    2
3. Exercises
Find the following limits

1. lim x
      1
   x→− 3
                            -1/3

2. lim π
   x→−1

        3x + 7
3. lim                      19/5
   x→4 x + 1

         x + 15
4. lim
   x→4     3
          5− x
5. lim
   x→−6    2
3. Exercises
Find the following limits

1. lim x
      1
   x→− 3
                            -1/3

2. lim π
   x→−1
                             π
        3x + 7
3. lim                      19/5
   x→4 x + 1

         x + 15
4. lim
   x→4     3
          5− x
5. lim
   x→−6    2
3. Exercises
Find the following limits

1. lim x
      1
   x→− 3
                            -1/3

2. lim π
   x→−1
                             π
        3x + 7
3. lim                      19/5
   x→4 x + 1

         x + 15             19
4. lim
   x→4     3                     3
          5− x
5. lim
   x→−6    2
3. Exercises
Find the following limits

1. lim x
      1
   x→− 3
                            -1/3

2. lim π
   x→−1
                             π
        3x + 7
3. lim                      19/5
   x→4 x + 1

         x + 15             19
4. lim
   x→4     3                     3
          5− x              11
5. lim
   x→−6    2                     2
Day 32
1. Limits
Find the following limit




                   2
            x −1
       lim
        x→1 x − 1
Day 32
1. Limits
Find the following limit




                   2
            x −1
       lim
        x→1 x − 1
1. Limits
Find the following limits


               2
       x − 5x − 6
1. lim
   x→6     x−6
         3
        x −1
2. lim
    x→1 x − 1
1. Limits
Find the following limit


                                    x +1
                           lim
                           x→−1 3 −   x + 10
2. Limits - Exercises
Find the following limits:

          3h
1.   lim
     h→0 h

           x−3
2.   lim 2
      x→3 x − 9
            2
           x + 7x
3.   lim
      x→0     x
               x +1
4.    lim
      x→−1 3 −   x + 10
                    2        2
5.   lim
         ( x + h)       −x
     h→0          h
Day 33
1. Limits
Find the following limit




                   2
            x −1
       lim
        x→1 x − 1
Day 33
1. Limits
Find the following limit




                   2
            x −1
       lim
        x→1 x − 1

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PM5006 Week 7

  • 1. Day 31 1. Limits - Exercises True or False: ! f (3) = 7 DNE ! f (3) Undefined
  • 2. Day 31 1. Limits - Exercises True or False: ! f (3) = 7 False DNE ! f (3) Undefined
  • 3. Day 31 1. Limits - Exercises True or False: ! f (3) = 7 False False DNE ! f (3) Undefined
  • 4. Day 31 1. Limits - Exercises True or False: ! f (3) = 7 False False False DNE ! f (3) Undefined
  • 5. Day 31 1. Limits - Exercises True or False: ! f (3) = 7 False False False DNE ! f (3) Undefined True
  • 6. Day 31 1. Limits - Exercises True or False: ! f (3) = 7 False False False DNE ! f (3) Undefined True False
  • 7. Day 31 1. Limits - Exercises True or False: ! f (3) = 7 False False False DNE ! f (3) Undefined True False True
  • 8. 1. Limits - Exercises True or False: ! f (0) = 5 DNE f (3) Undefined
  • 9. 1. Limits - Exercises True or False: ! f (0) = 5 False DNE f (3) Undefined
  • 10. 1. Limits - Exercises True or False: ! f (0) = 5 False False DNE f (3) Undefined
  • 11. 1. Limits - Exercises True or False: ! f (0) = 5 False False True DNE f (3) Undefined
  • 12. 1. Limits - Exercises True or False: ! f (0) = 5 False False True DNE f (3) Undefined True
  • 13. 1. Limits - Exercises True or False: ! f (0) = 5 False False True DNE f (3) Undefined True True
  • 14. 1. Limits - Exercises True or False: ! f (0) = 5 False False True DNE f (3) Undefined True True False
  • 15. 2. Notes Find the following limit 2 lim 2x − 3x − 4 x→−1
  • 16. 2. Notes Find the following limit 2 lim 2x − 3x − 4 x→−1
  • 17. 3. Exercises Find the following limits 1. lim x 1 x→− 3 2. lim π x→−1 3x + 7 3. lim x→4 x + 1 x + 15 4. lim x→4 3 5− x 5. lim x→−6 2
  • 18. 3. Exercises Find the following limits 1. lim x 1 x→− 3 -1/3 2. lim π x→−1 3x + 7 3. lim x→4 x + 1 x + 15 4. lim x→4 3 5− x 5. lim x→−6 2
  • 19. 3. Exercises Find the following limits 1. lim x 1 x→− 3 -1/3 2. lim π x→−1 3x + 7 3. lim 19/5 x→4 x + 1 x + 15 4. lim x→4 3 5− x 5. lim x→−6 2
  • 20. 3. Exercises Find the following limits 1. lim x 1 x→− 3 -1/3 2. lim π x→−1 π 3x + 7 3. lim 19/5 x→4 x + 1 x + 15 4. lim x→4 3 5− x 5. lim x→−6 2
  • 21. 3. Exercises Find the following limits 1. lim x 1 x→− 3 -1/3 2. lim π x→−1 π 3x + 7 3. lim 19/5 x→4 x + 1 x + 15 19 4. lim x→4 3 3 5− x 5. lim x→−6 2
  • 22. 3. Exercises Find the following limits 1. lim x 1 x→− 3 -1/3 2. lim π x→−1 π 3x + 7 3. lim 19/5 x→4 x + 1 x + 15 19 4. lim x→4 3 3 5− x 11 5. lim x→−6 2 2
  • 23. Day 32 1. Limits Find the following limit 2 x −1 lim x→1 x − 1
  • 24. Day 32 1. Limits Find the following limit 2 x −1 lim x→1 x − 1
  • 25. 1. Limits Find the following limits 2 x − 5x − 6 1. lim x→6 x−6 3 x −1 2. lim x→1 x − 1
  • 26. 1. Limits Find the following limit x +1 lim x→−1 3 − x + 10
  • 27. 2. Limits - Exercises Find the following limits: 3h 1. lim h→0 h x−3 2. lim 2 x→3 x − 9 2 x + 7x 3. lim x→0 x x +1 4. lim x→−1 3 − x + 10 2 2 5. lim ( x + h) −x h→0 h
  • 28. Day 33 1. Limits Find the following limit 2 x −1 lim x→1 x − 1
  • 29. Day 33 1. Limits Find the following limit 2 x −1 lim x→1 x − 1

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