Limit Question and Solution from Book - High Resolution Picture

  • Thread starter transgalactic
  • Start date
  • Tags
    Limit
In summary, the question is asking how the engineers got "e" and why the solution of just input (pi/4) instead of X doesn't work. The answer is that you cannot actually do that, because tan(pi/2) is not 0 but infinity,so any number raised to the power of infinity is actually undefined.
  • #1
transgalactic
1,395
0
i added a file with a question and a solution from my book

i added in te file some questions about their solution

its a high resolution picture
you can zoom on it.

http://img136.imageshack.us/my.php?image=img6685ji1.jpg
 
Physics news on Phys.org
  • #2
I have absolutely NO idea how the working at the beginning of the picture relates to showing [tex]\lim_{x\to 0} (1+x)^{1/x} = e[/tex].

However the e limit is quite easy to show if you use the nice property of the natural logarithm, [tex]\log_e \lim_{x\to a} f(x) = \lim_{x\to a} \log_e f(x)[/tex]. In other words, you can interchange the order of limits and logs.

EDIT: O I did forget to mention you might have to use [tex]\ln(1+x)=\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} x^n = x - \frac{x^2}{2} + \frac{x^3}{3} - \cdots \quad{\rm for}\quad \left|x\right| \leq 1\quad {\rm unless}\quad x = -1[/tex], and some people may see that method as somewhat circular, depending on what definitions are used, what is already proved etc etc. But it should be fine.
 
  • #3
i am puzzled too about it

how did they get "e"?

and why the solution of just input (pi/4) instead of X doesn't work?
that way we get (2.41)^0 that's an possible answer to?
 
Last edited:
  • #4
What I am puzzled about is what that chunk of working is even about? It doesn't seem to relate to the second part, and even that chunk in itself seems to be quite confusing. Just state the original question first please.
 
  • #5
the question is:

lim [tg(pi/8 + x) ] ^ (tg 2x )

x->(pi/4)
 
  • #6
transgalactic said:
i am puzzled too about it

how did they get "e"?

and why the solution of just input (pi/4) instead of X doesn't work?
that way we get (2.41)^0 that's an possible answer to?

well u cannot actually do that, because tan(pi/2) is not 0 but infinity,so any number raised to the power of infinity is actually undefined. so u have to express it in the form

e^tg2x ln tg(pi/8 +x)

and then take the limit as x-->pi/4
 
  • #7
i can't figure out a way to solve this question??
 

1. What is a limit question?

A limit question is a type of inquiry that involves determining the maximum or minimum value that a function can approach as the input approaches a certain value or as the output approaches infinity or negative infinity.

2. How do you solve a limit question?

To solve a limit question, you can use various techniques such as substitution, factoring, and algebraic manipulation. You can also use graphs, tables, or calculators to help visualize and approximate the limit value.

3. What is the importance of high resolution pictures in scientific research?

High resolution pictures are important in scientific research because they provide clear and detailed images that can reveal information and patterns that may not be visible in low resolution images. They can also help in accurately measuring and analyzing data, and in communicating research findings to a wider audience.

4. Where can I find high resolution pictures for my research?

High resolution pictures can be found in various sources such as scientific journals, online databases, and government or research institute websites. Some universities and libraries also have collections of high resolution images that can be accessed for research purposes.

5. How can I ensure the reliability and accuracy of high resolution pictures?

To ensure the reliability and accuracy of high resolution pictures, it is important to use images from reputable sources and to properly cite and verify the source of the image. It is also helpful to consult with experts in the field or to conduct additional research to confirm the validity of the image.

Similar threads

  • Other Physics Topics
Replies
5
Views
933
Replies
62
Views
3K
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
981
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Quantum Interpretations and Foundations
Replies
29
Views
2K
  • Electrical Engineering
Replies
4
Views
979
  • Calculus and Beyond Homework Help
Replies
2
Views
868
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
5K
Back
Top