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The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(a) = r where r is the unique remainder obtained when a is divided by b.
(a) What is the range of f? Based on your answer, is f onto?
(b) Determine whether f a 1-1 function.
Limits The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some
Logarithm Functions : In this section we'll discuss look at a function which is related to the exponential functions we will learn logarithms in this section. Logarithms are one o
nC6:n-3C3=91:4
the length of three pieces of ropes are 140cm,150cm and 200cm.what is the greatest possible length to measure the given pieces of a rope?
1. a) Find the shortest paths from r to all other nodes in the digraph G=(V,E) shown below using the Bellman-Ford algorithm (as taught in class). Please show your work, and draw t
Function composition: The next topic that we have to discuss here is that of function composition. The composition of f(x) & g(x) is ( f o g ) ( x ) = f ( g ( x )) In other
Jeff burns 500 calories per hour bicycling. How long will he have to ride to burn 750 calories? To find out the number of hours required to burn 750 calories, divide 750 throug
The Definition of the Limit In this section we will look at the precise, mathematical definition of three types of limits we'll be looking at the precise definition of limits
If the squared difference of the zeros of the quadratic polynomial x 2 + p x + 45 is equal to 144 , find the value of p.
Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section
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