LIMITS approaches o+ - how come?

  • Context: Undergrad 
  • Thread starter Thread starter noobie!
  • Start date Start date
  • Tags Tags
    Limits
Click For Summary
SUMMARY

The discussion focuses on the evaluation of limits, specifically the behavior of the function \( \lim_{x \to -8^+} \frac{2x}{x+8} \). Participants confirm that as \( x \) approaches -8 from the right, the limit results in negative infinity due to the numerator being negative and the denominator being a small positive number. Additionally, the limit of the expression \( \left(\frac{1}{x^{1/3}} - \frac{1}{(x-1)^{4/3}}\right) \) as \( x \) approaches 0 from both sides is discussed, with the conclusion that it leads to positive infinity.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with rational functions
  • Knowledge of approaching limits from the left and right
  • Basic graphing skills to visualize functions
NEXT STEPS
  • Study the concept of one-sided limits in calculus
  • Learn about the behavior of rational functions near vertical asymptotes
  • Explore graphical representations of limits using tools like Desmos
  • Investigate the properties of infinity in calculus
USEFUL FOR

Students studying calculus, educators teaching limit concepts, and anyone seeking to clarify their understanding of one-sided limits and rational functions.

noobie!
Messages
57
Reaction score
0
LIMITS approaches o+ - how come??

i encountered a few ques which makes me baffle whn i stdy about infinite limit.. as we know limit x --->0+ it will be positive infinity and when x-->o- it will be negative infinity; first of all m i rite?then..a que which i encountered was lim x --->-8+ (2x/ x+8) homework cum i get negative infinity instead of positive infinity?it makes me so confuse..so could any1 please rectify my mistakes for those theorem?please?! thanks a lot 1st..:confused:
 
Physics news on Phys.org


Well, what sign will a fraction between two negative numbers have? A negative sign, or a positive sign?
 


arildno said:
Well, what sign will a fraction between two negative numbers have? A negative sign, or a positive sign?

huh,umm i don't really get what u mean;but isit negative?:confused:
 


Intuitively, \lim_{x \to -8^+} 2x/(x+8) is what 2x/(x + 8) approaches as x approaches -8 from the right. If x is very slightly greater than -8, then 2x is negative (it's about -16), and x + 8 is a small positive number, so 2x/(x + 8) should be a large negative number. The graph below may help in visualizing what it looks like.

http://img380.imageshack.us/img380/7241/graphvn5.png
 
Last edited by a moderator:


adriank said:
Intuitively, \lim_{x \to -8^+} 2x/(x+8) is what 2x/(x + 8) approaches as x approaches -8 from the right. If x is very slightly greater than -8, then 2x is negative (it's about -16), and x + 8 is a small positive number, so 2x/(x + 8) should be a large negative number. The graph below may help in visualizing what it looks like.

http://img380.imageshack.us/img380/7241/graphvn5.png
[/URL]

thanks a lot..rite nw i have no doubts..thanks for your kind help..thanks..:wink:
 
Last edited by a moderator:


adriank said:
Intuitively, \lim_{x \to -8^+} 2x/(x+8) is what 2x/(x + 8) approaches as x approaches -8 from the right. If x is very slightly greater than -8, then 2x is negative (it's about -16), and x + 8 is a small positive number, so 2x/(x + 8) should be a large negative number. The graph below may help in visualizing what it looks like.

http://img380.imageshack.us/img380/7241/graphvn5.png
[/URL]

one more doubt is let say an example: [(1/x^1/3) - (1/(x-1)^4/3 ] ;its limit is x --->0+ and 0- so the answer will be positive infinity because of v sub x=o into the equation ,thus its infinity minus 3 that's why we got positive infinity same goes to 0- ?please rectify my mistakes if i have thm..thanks :blushing:
 
Last edited by a moderator:

Similar threads

MHB What is the Limit of (5x)/(100 - x) as x Approaches 100 from the Left?
  • · Replies 4 ·
Replies
4
Views
1K
MHB How to Find the Limit of (1 - x)/[(3 - x)^2] as x Approaches 3?
  • · Replies 5 ·
Replies
5
Views
1K
MHB What is the Limit of (3x)/(x-2) as x Approaches 2 from the Left?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad A question about limits and infinity
  • · Replies 7 ·
Replies
7
Views
2K
MHB Is the Limit of 1/(x^2 - 9) as x Approaches -3 from the Left Positive Infinity?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Is the Limit of 5/(x^2 - 4) as x Approaches 2 from the Right Positive Infinity?
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad How does the ratio test fail and the root test succeed here?
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Proving limit theorems when limit tends to infinity
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How Does the Limit of cosh and sinh Approach 1?
  • · Replies 4 ·
Replies
4
Views
17K
MHB Solve Limit w/o L'Hôpital: Miras Tussupov's Q on Yaoo Answers
  • · Replies 1 ·
Replies
1
Views
2K