Question about factoring for calculus

  • Thread starter Thread starter Checkfate
  • Start date Start date
  • Tags Tags
    Calculus Factoring
Click For Summary

Homework Help Overview

The discussion revolves around a calculus problem involving limits and factoring, specifically the expression lim(x->4) (k^2-16)/(sqrt(k)-2). Participants are exploring how to manipulate the expression to facilitate finding the limit.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to factor k^2-16 to simplify the limit expression. Some participants suggest using a multiplication technique to facilitate cancellation, while others caution against certain manipulations. There is also a reference to a general formula for factoring differences of squares.

Discussion Status

The discussion is active, with participants offering various approaches and considerations. There is a mix of suggestions regarding how to proceed with the problem, and some participants express uncertainty about their previous knowledge related to the topic.

Contextual Notes

Participants note that the problem may not be covered in standard textbooks, leading to some confusion about the necessary techniques for solving it. There is also an acknowledgment of prior learning expectations that may not have been met.

Checkfate
Messages
149
Reaction score
0
Hello, I have been reading these forums for quite a while now and am very impressed! I have a question :) I need to find the lim(x->4) (k^2-16)/(sqrt(k)-2) How would I go about factoring k^2-16 so that I can get sqrt(k)-2 on the numerator? Thanks!
 
Last edited:
Physics news on Phys.org
[tex]\left(\sqrt{k}\right)^4 = k^2[/tex] and [tex]2^4 = 16[/tex].
 
i would multiply the fraction by 1, where 1 = (sqrt(x) + 2)/(sqrt(x) + 2)

i guess that's the 1st step & the only tricky part. isn't this in your textbook?
 
Thankyou both. No unfortunately it is not in my textbook. I am using my father's calculus book from university as a supplement to my regular calculus material. It was probably assumed that I knew how to solve it so it wasn't even mentioned. Unfortunately I forgot how to solve it! Anyways, thanks.
 
something you might have noticed is that it would be a very BAD idea to multiply the sqrt(x)+2 into the numerator, and probably not a good idea in general to do that. factor the x^4 - 16 & only multiply the denominators to get what you want to cancel.
 
At some point prior to taking calculus, you should have learned the general formula (a2- b2)= (a- b)(a+ b).
 

Similar threads

Replies
4
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 3 ·
Replies
3
Views
1K
Replies
20
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 17 ·
Replies
17
Views
2K
Replies
29
Views
3K