## anonymous one year ago Need Help! Find the limit of the limit below

1. anonymous

|dw:1439230879897:dw|

2. hartnn

when v->4+ means v is very very near to 4, but greater than 4. agreed?

3. anonymous

Yep

4. hartnn

so, 4-v will be positive or negative?

5. anonymous

negative?

6. hartnn

thats right :) and since the denominator is having a modulus, it will be positive only. so our final answer will be negative!

7. anonymous

|dw:1439231347038:dw|

8. anonymous

I understand by writing things out..

9. hartnn

i meant |4-v| is always positive and 4-v is negative

10. anonymous

So how would I solve it?

11. hartnn

4-v from numerator and denominator would cancel out, so the answer would be either +1 or -1 the numerator is negative, and denominator is positive, so the overall answer is negative, that is -1.

12. anonymous

Are you sure it's that simple?

13. hartnn

yep!

14. anonymous

|dw:1439231746924:dw|Is that how the work would look like?

15. hartnn

ok, lets make some steps, since v is very near to 4, but greater than 4, lets take v = 4 + $$\delta$$ when $$v \to 4^+$$, $$\delta \to 0$$ |dw:1439231931131:dw| try to simplify that ^^

16. anonymous

1?

17. hartnn

the numerator simplifies to $$-\delta$$ and the denominator simplifies to $$|-\delta | = \delta$$ isn't it ?

18. hartnn

|dw:1439232227653:dw|

19. anonymous

I see it now! thanks for the clear work

20. hartnn

welcome ^_^