Complex Limit Problem

[ebowden1092]

lim. (a/(3-a)-2)/(a-2). (I do know what to do here, I just don't know how to factor the expression in the numerator)
a-->2

 

[Deleted member 4993]

lim. (a/(3-a)-2)/(a-2). (I do know what to do here, I just don't know how to factor the expression in the numerator)
a-->2

\(\displaystyle \lim_{a\to 2}\left[\frac{\frac{a}{3-a}-2}{a-2}\right]\)

You said:

I do know what to do here

Please share your thoughts - "show"us what you do know and where you are stuck after that.

 

[joshuaa]

if you look the other way, you will find that it is not a complex limit. in fact, one of the easiest limit one can find

 

[Steven G]

\(\displaystyle \lim_{a\to 2}\left[\frac{\frac{a}{3-a}-2}{a-2}\right]\)

You said:

I do know what to do here

Please share your thoughts - "show"us what you do know and where you are stuck after that.

lim. (a/(3-a)-2)/(a-2). (I do know what to do here, I just don't know how to factor the expression in the numerator)
a-->2

Thought process: a= 2 makes the denominator = 0.
Does it make the numerator =0? If no, then you are done and the answer is ____?
If a=2 makes the numerator not 0, then you can factor out (a-2) from the numerator and denominator. Then repeat.

Alternative you can get rid of that denominator in the numerator and then follow my process above.

 

[walter-]

lim. (a/(3-a)-2)/(a-2). (I do know what to do here, I just don't know how to factor the expression in the numerator)
a-->2

To what can you bring the numerator?

 

[NIPUL JARIWALA]

 

[lookagain]

One of the simplest math problems.View attachment 21440

NIPUL JARIWALA, this may be one of the simplest limit problems for you,
but do not impose that on the person asking the question. It was only asked
yesterday, the person asked was given a prompt to show some work, did not, so
you should not have given a full solution here at this time.

Also, when you write your lower case a letters, make sure to close them up so
that they do not resemble fours.