Limit of 3x/(5-x) as x approaches 5+ in Calculus

  • Thread starter Thread starter Kinetica
  • Start date Start date
  • Tags Tags
    Limit
Click For Summary
SUMMARY

The limit of the function 3x/(5-x) as x approaches 5 from the right (5+) is confirmed to be negative infinity. As x approaches 5, the denominator (5-x) approaches zero from the negative side, resulting in a division by a very small negative number. Consequently, the expression evaluates to 15 divided by a value approaching zero, leading to the conclusion that the limit is indeed negative infinity.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with rational functions
  • Knowledge of approaching limits from the left and right
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the concept of one-sided limits in calculus
  • Explore the behavior of rational functions near vertical asymptotes
  • Learn about the epsilon-delta definition of limits
  • Investigate other examples of limits approaching infinity
USEFUL FOR

Students studying calculus, particularly those focusing on limits and rational functions, as well as educators looking for examples to illustrate limit behavior in mathematical analysis.

Kinetica
Messages
83
Reaction score
0

Homework Statement



lim x->5+

3x/(5-x)


Homework Equations





The Attempt at a Solution


Is this a straight forward solution,
-infinity?
Because 3*5=15, and if x approaches 5 from the positive side, it means that (5-x)=-0.000000000001
So, 15/-000000000000.1 = -infinity
 
Physics news on Phys.org
yep, that's right. I don't know why the somebody chose to make such a trivial example into a problem, but whatever.
 
I expected to have some tricks in this problem...
 

Similar threads

  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
2
Views
2K
Replies
8
Views
2K