## haterofmath 3 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. hsmt

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

2. hsmt

are you there?

3. hsmt

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

4. haterofmath

i'm not sure

5. hsmt

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

6. haterofmath

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

7. hsmt

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

8. haterofmath

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

9. haterofmath

-infity

10. hsmt

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

right hand

12. hsmt

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

13. hsmt

what is the graph of that function?

14. haterofmath

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

15. hsmt

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

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

oh ok

18. hsmt

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

19. hsmt

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

yea

21. hsmt

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

if so, what did you get for a value?

23. haterofmath

39

24. hsmt

that would be the correct answer. nicely done.

25. haterofmath

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

26. hsmt

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

27. haterofmath

lol. no not tonight

28. hsmt

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

29. haterofmath

thanks and the same to you

30. hsmt

:))

31. haterofmath

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