## anonymous one year ago Please help me : find the limit lim (10/ln|x|) as x approaches to +infinity and then as x approaches to - infinity

1. hartnn

just plug in whats $$\ln(\infty )$$

2. anonymous

lim

3. anonymous

lim 10/ln|x|

4. hartnn

yeah, thats the question, when you plug in the value of x. you get 10/ln |infinity| you can find that value if you know whats ln |infinity| = ...

5. anonymous

... and whats the limit of ln|infinity| ?

6. hartnn

let me ask this way, infinity represents a very large number so logarithm of a very large number is : (A) very large number or (B) very small number ?

7. anonymous

a ?

8. hartnn

yes so ln |infinity| = infinity! and whats 10/infinity??

9. anonymous

10. anonymous

it's the absolute value what really confuses me

11. hartnn

yes, 10 divided by a very large number = very small number = 0

12. anonymous

ok , then whats the difference between lim ln(infinity) and lim ln|infinity| ?

13. hartnn

|a| = a when a >= 0 and |a| = -a when a<0 example : |4| = 4, because 4 is >0 |-5| = -(-5) = 5 because -5 is <0 same goes for |infinity|