Maths problem set 1 | Mathematics homework help

 

 

Don't use plagiarized sources. Get Your Custom Essay on
Maths problem set 1 | Mathematics homework help
Just from $13/Page
Order Essay

 

  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 

 

 

 

 

 

 

 

 

 

 

 

Calculator

Calculate the price of your paper

Total price:$26
Our features

We've got everything to become your favourite writing service

Need a better grade?
We've got you covered.

Order your paper