How to Find the Limit of (1 - x)/[(3 - x)^2] as x Approaches 3?

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Discussion Overview

The discussion revolves around finding the limit of the function (1 - x)/[(3 - x)^2] as x approaches 3. Participants explore various methods to determine the limit, including algebraic reasoning, graphical analysis, and the use of tables of values.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant suggests that the limit is negative infinity based on a graphical representation of the function.
  • Another participant questions the inability to find the limit using algebra, proposing that as the denominator approaches zero, the overall value of the function must increase or decrease significantly.
  • Some participants express frustration over the need for a table of values, arguing that the limit has already been established as negative infinity due to the behavior of the denominator and the sign of the function.
  • There are repeated calls for understanding and patience, particularly from those learning the material independently.

Areas of Agreement / Disagreement

Participants generally agree that the limit approaches negative infinity, but there is disagreement on the necessity of using algebra or tables of values to arrive at this conclusion. The discussion remains somewhat unresolved regarding the best method to find the limit.

Contextual Notes

Some participants express confusion about algebraic methods and the implications of dividing by small numbers, indicating a potential gap in understanding the underlying concepts of limits.

nycmathdad
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Find the limit of (1 - x)/[(3 - x)^2] as x---> 3.

I could not find the limit using algebra. So, I decided to graph the given function.
I can see from the graph on paper that the limit is negative infinity.
How is this done without graphing?
 
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Problem 1.5.35.
Odd numbered.
Look up the answer.
 
I don't understand why you can't find the answer using algebra?

If you divide by a big number, your total amount is small.

If you divide by a small number, your total amount is big.

Here, the denominator is getting closer to 0 (so very small), so what do you think happens to the whole amount?
 
Prove It said:
I don't understand why you can't find the answer using algebra?

If you divide by a big number, your total amount is small.

If you divide by a small number, your total amount is big.

Here, the denominator is getting closer to 0 (so very small), so what do you think happens to the whole amount?

I am learning this material on my own with very limited time on my hand. Be a little more understanding in your reply. The limit is negative infinity. How is this done using a table of values?
 
nycmathdad said:
I am learning this material on my own with very limited time on my hand. Be a little more understanding in your reply. The limit is negative infinity. How is this done using a table of values?

Why do you need a table of values at all? You have already established that the limit is $-\infty$ because the denominator gets extremely small, and the function has negative values on both sides.
 
Prove It said:
Why do you need a table of values at all? You have already established that the limit is $-\infty$ because the denominator gets extremely small, and the function has negative values on both sides.

Ok. Take it easy, bro. Happy Resurrection Sunday. Relax.
 

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