Multivariable Limits examples and sq. thm

In summary, the student is preparing for their calculus 3 exam and is looking for practice problems involving limits with sin/cos/tan. They have tried searching online, but have not found many examples with solutions. They are also unsure when to use the squeeze theorem and are seeking guidance on identifying opportunities to use it.
  • #1
texas
1
0
So I'm trying to study for my calc 3 exam, but I have noticed that my book doesn't have many limit questions that use sin/cos/tan, but I know those will likely be on the test. I have tried to google but I can't find many examples that have solutions. Are there any free sites that have problems to help me practice?

Also, I can't seem to figure out when to use the squeeze theorem. In general, when do you look for it?
 
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  • #2
texas said:
So I'm trying to study for my calc 3 exam, but I have noticed that my book doesn't have many limit questions that use sin/cos/tan, but I know those will likely be on the test. I have tried to google but I can't find many examples that have solutions. Are there any free sites that have problems to help me practice?
Well, I can think of one REALLY good one that's open in your browser right now. :biggrin:

I periodically stalk the forums here looking for something fun to occupy my time.

texas said:
Also, I can't seem to figure out when to use the squeeze theorem. In general, when do you look for it?
When you recognize a function ##h## that is always greater than or equal to ##f## on an interval ##I## and a function ##g## that is always less than or equal to ##f## on the same interval, you might think about using it. The key is to get a ##g## and ##h## that have limits equal to each other at the point you want to take the limit of ##f## at in ##I##.
 

1. What is a multivariable limit?

A multivariable limit is a mathematical concept that describes the behavior of a function as it approaches a specific point in a multi-dimensional space. It is denoted by the notation "lim(f(x,y), (a,b))" and is used to determine the value of a function at a specific point.

2. How is a multivariable limit calculated?

To calculate a multivariable limit, you must approach the point of interest along various paths and determine if the function approaches a single value or if it has different values along different paths. If the function approaches a single value, that value is the limit. If the function has different values along different paths, the limit does not exist.

3. What is the squeeze theorem and how is it used in multivariable limits?

The squeeze theorem, also known as the sandwich theorem, states that if two functions have the same limit at a point and a third function is between them, then the third function must also have the same limit at that point. In multivariable limits, the squeeze theorem is used to prove the existence of a limit at a particular point.

4. Can you provide an example of a multivariable limit?

One example of a multivariable limit is the function f(x,y) = x^2 + y^2. As x and y approach the point (2,3), the function approaches a single value of 13. This can be seen by approaching the point along different paths, such as the x-axis and y-axis, and observing that the function approaches the same value.

5. What is the significance of multivariable limits in scientific research?

Multivariable limits are important in scientific research as they allow us to understand the behavior of functions in multi-dimensional spaces. They are used in fields such as physics, engineering, and economics to analyze the behavior of complex systems and make predictions about their future behavior.

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