find the indicated one-sided limit. if the limiting value is inifinte indicate whther is is +∞or− ,
lim x→4 (3x−9)

- anonymous

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- anonymous

hi. i have a question. is the limit being taken from the left or right?

- anonymous

are you there?

- anonymous

well, this is a linear function or a first degree polynomial.

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## More answers

- anonymous

i'm not sure

- anonymous

so tell me what the problem is asking, if you would be so kind.

- anonymous

\[\lim_{x \rightarrow 4}(3x^2-9) \]

- anonymous

can you tell me in words, what it is asking?

- anonymous

find the indicated one-sided limit. if the limiting value is inifinte, indicate whether it is \[+\infty or -\]

- anonymous

-infity

- anonymous

ok. so they want the limit of 3x^2-9 as x approaches 4. I see the 4, but is it a left- or right hand + limit. My glasses may not be picking up the detail.

- anonymous

right hand

- anonymous

ok. perfect. now, what do we know about 3x^2-9? what kind of a function is it?

- anonymous

what is the graph of that function?

- anonymous

i'm not sure...i'm a little confused on the whole topic of limits

- anonymous

it is ok. it is a second degree polynomial. i am stating it this way because there is a limit theorem that states that all polynomial functions are continuous and all polynomial functions have equal left and right hand limits at every point in their domain.

- anonymous

this function would graph out to be a parabola. Furthermore, unless special domains are part of the problem, you simply substitute the x value into the expression to get the limit.

- anonymous

oh ok

- anonymous

incidentally, polynomial functions are any function that can be written in the form:
y=ax^n+bx^(n-1)+...+c

- anonymous

so, 5x^6+3x^5+4=y is a sixth degree polynomial function. notice the degree and the highest power are the same.

- anonymous

yea

- anonymous

ok. the only reason i bring this up is because they tend to throw a lot of these polynomial functions at you in calc classes. now back to the problem at hand. did you substitute 4 for x in the expression?

- anonymous

if so, what did you get for a value?

- anonymous

39

- anonymous

that would be the correct answer. nicely done.

- anonymous

ok..thanks...its all starting to make sense now

- anonymous

good. do you have any other questions? I am not paid by the hour lol

- anonymous

lol. no not tonight

- anonymous

well, then, i hope you have a lovely evening. take care and good nite

- anonymous

thanks and the same to you

- anonymous

:))

- anonymous

what happens if the limit is being taken from the left?

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