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

1. hsmt Group Title

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

2. hsmt Group Title

are you there?

3. hsmt Group Title

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

4. haterofmath Group Title

i'm not sure

5. hsmt Group Title

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

6. haterofmath Group Title

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

7. hsmt Group Title

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

8. haterofmath Group Title

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

9. haterofmath Group Title

-infity

10. hsmt Group Title

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. haterofmath Group Title

right hand

12. hsmt Group Title

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

13. hsmt Group Title

what is the graph of that function?

14. haterofmath Group Title

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

15. hsmt Group Title

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. hsmt Group Title

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. haterofmath Group Title

oh ok

18. hsmt Group Title

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

19. hsmt Group Title

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

20. haterofmath Group Title

yea

21. hsmt Group Title

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. hsmt Group Title

if so, what did you get for a value?

23. haterofmath Group Title

39

24. hsmt Group Title

that would be the correct answer. nicely done.

25. haterofmath Group Title

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

26. hsmt Group Title

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

27. haterofmath Group Title

lol. no not tonight

28. hsmt Group Title

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

29. haterofmath Group Title

thanks and the same to you

30. hsmt Group Title

:))

31. haterofmath Group Title

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