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For the following function, find the IROC using the limit definition at the indicated value. If possible, use algebra to find the limit: ( ) = 2 2 − 3 at = −1

1.    Draw a  possible graph of f(x) given the following limits. All of these limits apply to the same graph.

2.      Graph and evaluate the limits.

 

 

  2 − 1            ≤ −1

( ) =− 2 + 2    − 1 < ≤ 1

           −3 + 1              > 1

 

 

a)     

 

 

b)   lim ( ) →−1

 

 

c)     

d)   

e)  a.      lim ( ) →∞

 

 


 

For each of the following functions, find the IROC using the limit definition at the indicated value. Where possible, use algebra to find the limit. Where algebra is not possible, use a table or a graph to find the limit. #3-#6 you should be able to do algebraically, #7 and # 8 you will need to set up AROC and put a small number in for h and calculate the AROC and that will be a good estimate of IROC at the desired point.

3.      ( ) = 2 2 − 3 at = −1  


7.  ( ) = 3 = −2                                                     

  8.  ℎ( ) = sin( ) =

 

 

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