Maths Problem Set 1
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Prove that is one-to-one function.
Let f:, as given below. Is f a one-to-one function? Please explain why or why not.
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.
- If n is fixed as 5, is this function one-to-one?
- List five numbers that have the exact same image.
Find
Find
Find
Find as
Prove that is a continuous function.
Find derivatives of the following functions using differentiation rules. (Do not use the definition of a derivative!)
Find the derivative of the following function at :
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)
Let and , where. Find and as well as the domain and range of these functions.
Find the derivative of by using the definition of the derivative
- 10 years ago
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