1. Prove that  is one-to-one function.                 

     

  2. Let f:, as given below.  Is f a one-to-one function?  Please explain why or why not.                                                                                                                                 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


  1. The modulo function (a mod n or a modulo n) maps every positive integer number to the remainder of the division of a/n.    For example, the expression 22 mod 5 would evaluate to 2 since 22 divided by 5 is 4 with a remainder of 2.  The expression 10 mod 5 would resolve to 0 since 10 is divisible by 5 and there is not a remainder.

 

    1. If n is fixed as 5, is this function one-to-one?             

 

 

 

    1. List five numbers that have the exact same image.  

 

 

 

 

 

  1. Find    

                                                                                           

     

  2. Find                 

                                                                                           

     

  3. Find           

                                                                                           

     

  4. Find   as       

           

     

  5. Prove that  is a continuous function. 

     

  6. Find derivatives of the following functions using differentiation rules.  (Do not use the definition of a derivative!)

     

 

    1.    

 

 

 

                                                               

 

    1.   

 

 

 

                               

 

    1.         

 

 

 

                                               

 

 

 

 

                                                                                               

 

 

 

 

                                                                               

 

    1.   

 

 

 

                                                               

 

    1.             

 

 

 

                                 

 

    1.       

 

                                                               

 

 

 

  1. Find the derivative of the following function at :     

                                                                           

     

  2. Find the derivative of the following function   using the definition of a derivative.  (Hint: though you can use the rules of differentiation to check your answer, you must use the definition of a derivative to solve this problem in order to receive any credit for your response)   

                                           

     

  3. Let   and , where.   Find  and as well as the domain and range of these functions.

     

  4. Find the derivative of  by using the definition of the derivative 

 

 

 

 

 

 

 

 

 

 

 

  • 10 years ago
Maths Problem set1 Solution
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