## Babynini one year ago Limits....again. Help!

1. Babynini

Both numbers 6 and 7, but let's begin with 6!!

2. Babynini

@peachpi @zepdrix :)

3. Astrophysics

L'hospital for first one

4. Babynini

#6) b = 4?

5. zepdrix

Ya :) Imma wait and see what Ganeshie has to say though ^^

6. ganeshie8

Notice that the denominator is 0 when you plugin x=0 Also, for the limit to exist (finite), you must get the indeterminate 0/0 form when you plugin x=0. otherwise the limit does not exist (infinite). so, the numerator part must evaluate to 0 at x=0

7. ganeshie8

$$\sqrt{ax+b}-2$$ evaluating it at $$x=0$$ and setting equal to $$0$$ does give you $$b=4$$

8. ganeshie8

plugin the $$b$$ value, rationalize and you will see what $$a$$ needs to be

9. Astrophysics

For 7 note this |dw:1444533414414:dw| you can do the same with |2x-1| you'll have an ugly numerator at the beginning, but it'll simplify to something nice :D

10. Babynini

Right, so I got b. But the a is being something terrible.

11. ganeshie8

$\frac{\sqrt{ax+4}-2}{x}=\frac{ax+4-4}{x(\sqrt{ax+4}+2)} = \frac{a}{\sqrt{ax+4}+2}$ plugin x=0 and you will see immediately that $$a$$ needs to be $$4$$

12. dan815

|dw:1444533867422:dw|

13. Babynini

@ganeshie8 thanks! I got it :)

14. Babynini

@dan815 gwow you are doing some fancy stuff, I think I also follow wht you are doing :D

15. Babynini

mm well if a = 4 and b = 4..then it works.

16. Babynini

but it's always over 0 :/

17. Astrophysics

a should be 4

18. Babynini

Ok, yeah that's what I got xD thanks yall :)

19. dan815

you actully do get a limit!

20. dan815

|dw:1444534732654:dw|

21. dan815

okay i hope thats clear now

22. dan815

i think this is how lhopital is justified too

23. dan815

we are looking at the behavior of your function very locally, so we'd only care about the slopes changes around that point

24. Babynini

Righto, 6 all makes sense :) I'm going to start a new thread for number 7

25. dan815

so for example the lhopital way d/x(abs(2x-1)- abs(2x+)) --------------------- d/dx(x) d/dx ( abs(2x-1) - d/dx(abs(2x+1)) ------------------------------- 1 now derivative of abs(2x-1) near 0 = is -2 and the detiaive of abs(2x+1) near 0 is 2 so -2 - 2 ------- 1 =-4 as x-->0

26. Babynini

Em, haven't learnt derivatives yet :/

27. dan815

okay then do it the other way

28. Astrophysics

I think multiplying by conjugate might work

29. dan815

yeah