Final answer:
The interval of possible values for (b-a)/(1-ab) given 0≤a≤b≤1 is [0, 1), where 0 is included, and 1 is not, due to the constraints on a and b.
Step-by-step explanation:
To find the interval of (b-a)/(1-ab) values given that 0≤a≤b≤1, we need to consider the restrictions on a and b. Since ab cannot equal 1 to avoid division by zero, the maximum value of a and b is slightly less than 1, which limits the range of (b-a)/(1-ab). Looking at the expression, if a = 0, the fraction simplifies to b, which ranges between 0 and 1. However, if a approaches b, the numerator approaches 0, and the expression approaches 0. Unlike the numerator, as a approaches b, the denominator (1-ab) approaches 1-(b^2), which also ranges between 0 and 1. Therefore, the denominator will always be positive.
The maximum value of the expression occurs when b approaches 1 and a approaches 0, then (b-a)/(1-ab) approaches 1/(1-0) = 1. Hence, the range of values for this expression is from 0 to 1. Please note that the value each fraction approaches its minimum and maximum is based on the limits of a and b as they approach each other and the bounds of the interval [0,1].
Therefore, the interval of possible values for (b-a)/(1-ab) is [0, 1), where 0 is included in the interval, and 1 is not, given the constraints that 0≤a and a≤b≤1.