## chemmaj88 3 years ago At what POINTS is this function continuous..y=cosx/x...someone please explain to me how to solve these types of problems? is it whatever numbers make this an undefined problem?

1. ChrisV

well x=/=0

2. ChrisV

i would say limit x>0 $(-\infty,0)$$(0,\infty)$

3. ChrisV

but im a nub so dont trust me much

4. chemmaj88

the book says all x except x=0 so yes ur on it, but like, do u just see this problem n knw, or do u go thru a guess n check process, what process do u go thru to get an answer for these types of problems?

5. ChrisV

well the denominator can never be 0

6. ChrisV

so x cannot be 0

7. ChrisV

not much to guess at really

8. ChrisV

just means if x were zero

9. ChrisV

the value would be undefined

10. ChrisV

hence a hole in your graph

11. chemmaj88

got it! ok i got one more...

12. chemmaj88

y=sqrt(2x+3)

13. ChrisV

well since it is a square root is can never be negative

14. ChrisV

so it would be $(0,\infty)$

15. ChrisV

the graph of a square root function looks like

16. ChrisV

|dw:1328895361125:dw|

17. chemmaj88

the books answer is, all X greater than or equal to -3/2

18. ChrisV

yea thats right

19. ChrisV

because

20. ChrisV

y=sqrt(2x+3)

21. ChrisV

to make the square root 0 x would have to be -3/2

22. ChrisV

hence its still not a negative

23. ChrisV

been up all night sorry

24. ChrisV

getting tired

25. ChrisV

but since -3/2 make it the sqrt of 0 thats the limit

26. ChrisV

all other numbers have toi be greater then -3/2

27. chemmaj88

so if u plug in -3/2 "sqrt(2(-3/2)+3" this will equal 0?

28. ChrisV

yes because the 2's cancel

29. ChrisV

2x-3/2 = -3

30. ChrisV

-3+3 = 0

31. chemmaj88

got it! so on these types of problems are u really just looking for w/e numbers will make it undefined?

32. ChrisV

basically

33. ChrisV

and if you cannot make it undefined

34. ChrisV

its continuous from -inf to +inf

35. ChrisV

ok well you have a good one, gotta get some rest now

36. chemmaj88

thanks!