Maths Problems Set 1
Prove thatis 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
Findas
Prove thatis 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 functionusing 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)
Letand, where. Find and as well as the domain and range of these functions.
Find the derivative of by using the definition of the derivative
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Solution: Maths Problem set1 Solution