## anonymous one year ago Determine whether f(x) approaches negative or positive infinity as x approaches 4 from the left and right. f(x)= 1/(x-4)^2

1. anonymous

$f(x)=\frac{ 1 }{ x-4^{2} }$

2. hartnn

you know what "x approaches 4 from left" mean?

3. anonymous

In the negative direction, correct?

4. hartnn

yes, more precisely, it means value of x is very very very near to 4 but LESS than 4 like 3.9 or 3.9999999

5. anonymous

Okay, and from there I can come to the conclusion that it will be infinitely positive and infinitely negative as x approaches 4 from the left and right?

6. hartnn

woah! slow down.. there are 2 cases there when x approaches 4 from left, then is x-4 negative or positive?? is (x-4)^2 negative or positive?? based on that you will be able to tell, whether its +infinity or -infinity

7. hartnn

similarly, the other case when x approaches 4 from right, then is x-4 negative or positive?? is (x-4)^2 negative or positive?? based on that you will be able to tell, whether its +infinity or -infinity

8. anonymous

from the right is positive infinity and from the left is negative infinity?

9. hartnn

can you first answer these?? is x-4 negative or positive?? is (x-4)^2 negative or positive??

10. anonymous

using what values? 3.999?

11. hartnn

if you're consider x is approaching from left, then yes

12. anonymous

then x-4 would be negative (x-4)^2 is postive

13. hartnn

good! so for x approaching from left we get positive infinity :)

14. hartnn

now take x approaching from right case

15. anonymous

then it would be negative infinity

16. anonymous

I understand now, sorry for not understanding it until now and thank you for helping me!

17. hartnn

welcome ^_^

18. hartnn

but actually for right case also, it will be +infinity

19. hartnn

because (x-4)^2 will anyways be positive

20. hartnn

@Alyssa8

21. anonymous

im not that smart lol sorry