Question

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

Answer 1

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

Answer 2

are you there?

Answer 3

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

Answer 4

i'm not sure

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

-infity

Answer 10

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.

Answer 11

right hand

Answer 12

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

Answer 13

what is the graph of that function?

Answer 14

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

Answer 15

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.

Answer 16

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.

Answer 17

oh ok

Answer 18

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

Answer 19

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

Answer 20

yea

Answer 21

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?

Answer 22

if so, what did you get for a value?

Answer 23

39

Answer 24

that would be the correct answer. nicely done.

Answer 25

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

Answer 26

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

Answer 27

lol. no not tonight

Answer 28

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

Answer 29

thanks and the same to you

Answer 30

:))

Answer 31

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