# Maths problem set 1 | Mathematics homework help

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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

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