Determine if the set {0.5,1.2,4.7} is a partition of [0,4.7].

Primary tabs

Lesson Parent: 
Integration II: Partitioning the x-axis.
Problem: 

Determine if the set {0.5,1.2,4.7} is a partition of [0,4.7].

Answer: 

The set {0.5,1.2,4.7} is not a partition of [0,4.7].

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

Recall that a partition of [a,b] has the following properties:

  1. It includes the numbers a and b.
  2. The other elements of the partition are between a and b.

We typically write the partition such that <Sign in to see all the formulas>. If we do then both properties are automatically satisfied.

In this problem a=0 and b=4.7. First, note that 0 is not in the set <Sign in to see all the formulas>. Therefore, property 1 does not hold and <Sign in to see all the formulas> is not a partition of <Sign in to see all the formulas>. Since we already know that this is not a partition we do not need to check the second property. We have determined what the problem asked us to determine.