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					AP Calculus BC - Ahlborn                                             Problem Sheet - E



                                   PROBLEM SHEET E – Beyond the AP

                             1
1. Consider      lim             
                x  3     x3
     a. If N  40 , find δ .
     b. If N  1000 , find δ .

                               1
2. Prove that lim                         
                 x 6     ( x  6) 2

                               2
3. Prove that lim                         
                 x  5     ( x  5) 2

                                      x5      x 1
4.   lim f ( x )  5 where f x                  .
     x 1                            3  8 x   x 1

                                      x2      x0
5.   lim f ( x )  1 where f x                  .
     x 0
                                      x  0.5 x  0

                            2x  3
6. Prove that       lim            2
                 x       x2


                                                  Answers

1. a.    δ  .025


                        1
2. Choose δ 
                        N


                    1
4. Choose ε 
                    2




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