Limits - Please provide some good reading materials

In summary, the conversation is discussing the concepts of limits, specifically the L'Hospital rule and the product rule. The L'Hospital rule involves finding the limit of a quotient of two functions by taking the limit of their derivatives. The product rule states that the limit of a product of two functions is equal to the product of their limits, as long as both individual limits exist. The definition of "existing" in this context is a finite, non-zero value. The conversation also mentions looking into reading material on this topic, specifically calculus texts by James Stewart, Courant, and John.
  • #1
truewt
78
0
Can anyone provide me with insights on limits?

Like L' Hospital rule (don't know whether spelt right), and product rule such as [tex] lim_{x\rightarrow\a} [f(x)g(x)] = lim_{x\rightarrow\a} f(x) \cdot lim_{x\rightarrow\a} g(x) [/tex] should [tex] lim_{x\rightarrow\a} f(x) [/tex]and [tex]lim_{x\rightarrow\a} g(x) [/tex] exists.

And oh, the product rule, which I'm pretty sure I read from some course notes, stating that only when [tex]lim_{x\rightarrow\a} g(x) [/tex] and [tex] lim_{x\rightarrow\a} f(x) [/tex] exists, what is the definition of existing? A finite value? Non-zero?

Oh and could anyone provide me with some reading material on this topic?
 
Last edited:
Physics news on Phys.org
  • #2
Why can't my latex work?

Is that why no one is helping me here..
 
  • #3
I couldn't see your LaTex graphics, but Calculus texts by James Stewart (of the University of Waterloo, I believe) have good (possibly the best) reputation as introductory calculus texts, so you might want to have a look at them.
 
  • #4
i recommend courant and john.
 

FAQ: Limits - Please provide some good reading materials

What are limits in mathematics?

Limits in mathematics are a fundamental concept used to describe the behavior of a function as the input approaches a particular value or point. They are used to analyze the behavior of functions at specific points and to determine the overall behavior of a function as the input values get closer and closer to a particular value.

How do limits work?

Limits are typically evaluated using the limit notation, which consists of the function, the input value, and the limit symbol (lim). The limit notation is used to represent the behavior of a function as the input approaches a particular value. It is evaluated by finding the function's value at points closer and closer to the input value and observing the trend. If the values approach a finite number, the limit exists.

What is the difference between a limit and a derivative?

Limits and derivatives are related concepts, but they are not the same. A limit describes the behavior of a function as the input approaches a specific value, while a derivative describes the instantaneous rate of change of a function at a particular point. In other words, a limit gives a snapshot of a function's behavior, while a derivative shows how the function is changing at a specific point.

What are the common applications of limits?

Limits are used in various fields of mathematics, including calculus, algebra, and geometry. They also have many practical applications in physics, engineering, and economics. Some common applications of limits include finding the maximum or minimum of a function, calculating velocity and acceleration, and determining the convergence or divergence of a series.

Can you recommend any good reading materials on limits?

Some good reading materials on limits include "Calculus: Early Transcendentals" by James Stewart, "Calculus" by Michael Spivak, and "The Calculus Lifesaver: All the Tools You Need to Excel at Calculus" by Adrian Banner. Khan Academy and Paul's Online Math Notes also offer comprehensive tutorials and practice problems on limits.

Similar threads

I Some questions on l'Hôpital rules
Replies
9
Views
2K
Insights Can You Solve the Mathematical Mystery Behind the Art of Integration?
Replies
10
Views
4K
B Linearization of a function error viewed with differentials
Replies
14
Views
2K
B Applying L'Hospital's rule to Integration as the limit of a sum
Replies
18
Views
2K
What is the proof for the Product Rule in Calculus?
Replies
16
Views
4K
I Alternative Definitions of the Epsilon-Delta
Replies
25
Views
3K
Understand Squeeze Theorem: Less/Greater than Other Function?
Replies
9
Views
8K
A question about the L'Hopital's rule
Replies
1
Views
2K
Confusion regarding a proof for an infinite limit property.
Replies
2
Views
2K
A question on proving the chain rule
2
Replies
36
Views
3K

Hot Threads

Recent Insights

Back
Top