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

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hi. i have a question. is the limit being taken from the left or right?
are you there?
well, this is a linear function or a first degree polynomial.

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i'm not sure
so tell me what the problem is asking, if you would be so kind.
\[\lim_{x \rightarrow 4}(3x^2-9) \]
can you tell me in words, what it is asking?
find the indicated one-sided limit. if the limiting value is inifinte, indicate whether it is \[+\infty or -\]
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.
right hand
ok. perfect. now, what do we know about 3x^2-9? what kind of a function is it?
what is the graph of that function?
i'm not sure...i'm a little confused on the whole topic of limits
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.
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.
oh ok
incidentally, polynomial functions are any function that can be written in the form: y=ax^n+bx^(n-1)+...+c
so, 5x^6+3x^5+4=y is a sixth degree polynomial function. notice the degree and the highest power are the same.
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?
if so, what did you get for a value?
that would be the correct answer. nicely done.
ok..thanks...its all starting to make sense now
good. do you have any other questions? I am not paid by the hour lol
lol. no not tonight
well, then, i hope you have a lovely evening. take care and good nite
thanks and the same to you
what happens if the limit is being taken from the left?

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