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

1. anonymous

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

2. anonymous

are you there?

3. anonymous

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

4. anonymous

i'm not sure

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

-infity

10. 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.

11. anonymous

right hand

12. anonymous

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

13. anonymous

what is the graph of that function?

14. anonymous

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

15. 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.

16. 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.

17. anonymous

oh ok

18. anonymous

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

19. anonymous

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

20. anonymous

yea

21. 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?

22. anonymous

if so, what did you get for a value?

23. anonymous

39

24. anonymous

that would be the correct answer. nicely done.

25. anonymous

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

26. anonymous

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

27. anonymous

lol. no not tonight

28. anonymous

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

29. anonymous

thanks and the same to you

30. anonymous

:))

31. anonymous

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

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