Questions About Intervals in Calculus for 14 Year Olds

In summary, the conversation revolved around a problem involving intervals and the symbols for union and intersection. The problem was asking for the intersection of two intervals, but the answer given was for the union. The symbols "(" and "[" represent open and closed ends, respectively. A helpful method for solving unions and intersections is to draw a number line and plot both sets. The union is all the numbers in both sets, while the intersection is the common numbers.
  • #1
Ygmaince241
7
0
Ok, I'm very new to calculus, and was stuck on the very basics of it. I'm only 14, but am extremely interested in math and science. I was inspired to study calculus when reading a book named, "Five Equations that changed the World", by Michael Guillen. Now I was doing some problems involving intervals. The book tells me to sketch the sets. The one problem is (-3,2] U (1, 7]. What exactly does the U stand for? The answer they gave for the example was, (1,2]. I know "(" stands for an open end, and "[" stands for a closed end. How do these apply to the sets. I couldn't see how they got the answer. Please help.
 
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  • #2
[tex]\cup[/tex] is union.

But are you sure the problem didn't ask for the intersection, (-3, 2] [tex]\cap[/tex] (1, 7], of the intervals...?
 
Last edited:
  • #3
Ygmaince241 said:
Ok, I'm very new to calculus, and was stuck on the very basics of it. I'm only 14, but am extremely interested in math and science. I was inspired to study calculus when reading a book named, "Five Equations that changed the World", by Michael Guillen. Now I was doing some problems involving intervals. The book tells me to sketch the sets. The one problem is (-3,2] U (1, 7]. What exactly does the U stand for? The answer they gave for the example was, (1,2]. I know "(" stands for an open end, and "[" stands for a closed end. How do these apply to the sets. I couldn't see how they got the answer. Please help.
Like Muzza said, that answer only makes sense if they were asking for the intersection of the two intervals, not the union. I don't exactly understand your problem. Do you understand what "open end", "closed end", "intersection", and "union" mean?
 
  • #4
Omg, yes. The problem was asking for an intersection. Sorry for not being specific enough.
 
  • #5
Hey there Ygmaince241.

With the union and intersection symbols it's sometimes a bit hard to remember which is which. I always think of it this way: [tex]\cup[/tex]nion and i[tex]\cap[/tex]tersection.
 
  • #6
A good way to solve for unions and intersections (if you're really stuck) is to draw a number line with both sets on it. Union is all the numbers in both sets while intersection is the common numbers.
ex.
_____-1_____0_____1___
<~~~~~~~o (-infinity, 0) 0=open, •=closed
•~~~~~~~~~~> [-1, infinity)
Looking at this, you can clearly see that the intersection is [-1, 0) and the union is
(-infinity, infinity)
 

What are intervals in calculus?

Intervals in calculus refer to a range of values or numbers on a number line. In calculus, intervals are used to represent the domain or range of a function, or to indicate the interval on which a function is increasing or decreasing. Intervals can be open (not including the endpoints) or closed (including the endpoints).

How do you determine the interval of a function?

To determine the interval of a function, you must first find the domain of the function. This can be done by looking at the restrictions on the variables in the function. Once the domain is determined, the interval can be found by looking at the values of the function within that domain. The interval will include the lowest and highest values of the function within that domain.

What is the difference between an open and a closed interval?

An open interval does not include the endpoints, while a closed interval includes the endpoints. For example, an open interval of (0,5) would include all numbers between 0 and 5, but not including 0 or 5. A closed interval of [0,5] would include 0 and 5 as well as all numbers in between.

How are intervals used in calculus?

Intervals are used in calculus to represent the domain and range of a function, as well as to analyze the behavior of a function. Intervals can indicate where a function is increasing or decreasing, as well as where the function has local maximums and minimums. Intervals are also used in integration and differentiation to determine the behavior of a function over a specific range of values.

What are some real-world applications of intervals in calculus?

Intervals in calculus are used extensively in fields such as physics, engineering, and economics. For example, in physics, intervals can represent the time or distance over which an object is moving. In economics, intervals can represent the price or quantity of a good or service. Intervals are also used in statistics to represent confidence intervals for data analysis.

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