## anonymous 4 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. anonymous

well x=/=0

2. anonymous

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

3. anonymous

but im a nub so dont trust me much

4. anonymous

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. anonymous

well the denominator can never be 0

6. anonymous

so x cannot be 0

7. anonymous

not much to guess at really

8. anonymous

just means if x were zero

9. anonymous

the value would be undefined

10. anonymous

hence a hole in your graph

11. anonymous

got it! ok i got one more...

12. anonymous

y=sqrt(2x+3)

13. anonymous

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

14. anonymous

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

15. anonymous

the graph of a square root function looks like

16. anonymous

|dw:1328895361125:dw|

17. anonymous

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

18. anonymous

yea thats right

19. anonymous

because

20. anonymous

y=sqrt(2x+3)

21. anonymous

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

22. anonymous

hence its still not a negative

23. anonymous

been up all night sorry

24. anonymous

getting tired

25. anonymous

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

26. anonymous

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

27. anonymous

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

28. anonymous

yes because the 2's cancel

29. anonymous

2x-3/2 = -3

30. anonymous

-3+3 = 0

31. anonymous

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

32. anonymous

basically

33. anonymous

and if you cannot make it undefined

34. anonymous

its continuous from -inf to +inf

35. anonymous

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

36. anonymous

thanks!