Q:
# Why do we use minimum and maximum values when proving limits of Epsilon?

**People use minimum and maximum values when proving limits of epsilon, because epsilon is a range around a limit point.** To have a limit, one has to approach that limit from both the negative and positive directions.

Credit:
Jaap Hart
E+
Getty Images

In calculus, y= f(x). Limits describe the approach to a number on either side of the y-axis. For example, if f(x) equals x=1, but x does not equal 2, x becomes undefined when one gets to 2. It remains defined right up to the point at which one bumps into 2 on the x-axis. It resumes being defined as soon as one passes 2 on the x-axis. This means one can reach up to 2 without arriving at 2, for example,1.9, and one can reach 2 from the right side of the number line without actually getting there, for example, 2.1.

As one approaches a point on the x-axis, one is also approaching it from the f(x). So wherever one is on the x-axis, one is a corresponding distance away on the y-axis. Epsilon is the range approaching the limit from either a positive or negative direction. Because epsilon is a range of numbers, one has a maximum number and a minimum number.

Learn more about Calculus-
Q:
## How is the class midpoint calculated?

A: The class midpoint, or class mark, is calculated by adding the lower and upper limits of the class and dividing by two. The class midpoint is sometimes use... Full Answer >Filed Under: -
Q:
## What is the first octant?

A: In the context of solid three-dimensional geometry, the first octant is the portion under an xyz-axis where all three variables are positive values. Under ... Full Answer >Filed Under: -
Q:
## What are the x intercepts of a parabola?

A: The x intercepts of a parabola equation are the values of x for which y is equal to zero. These are the points at which the line of the parabola intercepts... Full Answer >Filed Under: -
Q:
## How do you find the interval of convergence?

A: Interval of convergence in a power series is the set of all values of a particular variable, usually x, for which the series converges. To determine the in... Full Answer >Filed Under: