Solving Infinite Limit Homework with Binomials: Step-by-Step Guide

  • Thread starter Thread starter Asphyxiated
  • Start date Start date
  • Tags Tags
    Infinite Limit
Click For Summary
SUMMARY

The limit problem discussed involves evaluating the expression \(\lim_{t \to 3^{+}} \frac {y+1}{(y-2)(y-3)}\). The initial attempt incorrectly simplified the denominator to \(y^{2}-5y+5\) and calculated the limit as \(-4\). However, the correct evaluation reveals that as \(y\) approaches 3 from the right, the denominator approaches zero, resulting in the limit approaching infinity. This highlights the importance of recognizing vertical asymptotes in limit problems.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with binomial expressions
  • Knowledge of vertical asymptotes
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the concept of vertical asymptotes in calculus
  • Learn about the behavior of limits approaching infinity
  • Practice solving limits involving binomials
  • Review algebraic manipulation techniques for rational functions
USEFUL FOR

Students studying calculus, particularly those focusing on limits and asymptotic behavior, as well as educators looking for examples of common pitfalls in limit evaluations.

Asphyxiated
Messages
263
Reaction score
0

Homework Statement



[tex]\lim_{t \to 3^{+}} \frac {y+1}{(y-2)(y-3)}[/tex]

Homework Equations





The Attempt at a Solution



I thought that this problem looked pretty straight forward but i am obviously doing something wrong. What I did was:

multiply the binomials:

[tex]\lim_{t \to 3^{+}} \frac {y+1}{y^{2}-5y+5}[/tex]

and then apply the limit:

[tex]\frac {3+1}{3^{2}-15+5} = \frac {4}{-1} = -4[/tex]

but this is WAY off because the answer is suppose to be infinity, so what did I forgot from the lesson?...
 
Physics news on Phys.org
Check your multiplication again.
 
ha, yep, ok thanks
 

Similar threads

Find limit of multi variable function
  • · Replies 10 ·
Replies
10
Views
2K
Solving a Limit Problem: Step-by-Step Guide
  • · Replies 3 ·
Replies
3
Views
2K
##\lim_{x \to0} \left(\dfrac{1}{\sin^2 x}-\dfrac{1}{x^2}\right)##
  • · Replies 5 ·
Replies
5
Views
2K
Evaluate the limit of this harmonic series as n tends to infinity
  • · Replies 17 ·
Replies
17
Views
3K
How should I show that these systems have no periodic solutions?
  • · Replies 2 ·
Replies
2
Views
2K
Determining domain for C^1 function
  • · Replies 4 ·
Replies
4
Views
1K
Limit problem involving two circles and a line
  • · Replies 8 ·
Replies
8
Views
2K
Proving differentiability for inverse function on given interval
  • · Replies 3 ·
Replies
3
Views
1K
Volume between a region (above x-axis and below parabola) and a surface
  • · Replies 4 ·
Replies
4
Views
3K
Problems solving a limit which results in an indeterminate form
  • · Replies 4 ·
Replies
4
Views
2K