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

[nycmathdad]

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?

 

[jonah1]

Problem 1.5.35.
Odd numbered.
Look up the answer.

 

[Prove It]

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?

 

[nycmathdad]

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?

 

[Prove It]

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.

 

[nycmathdad]

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.