## muffin Group Title Evaluate the limit, if it exists lim h-0 ((1/(x+h)^2 - 1/x^2 ))/ h 11 months ago 11 months ago

1. myininaya Group Title

Try combining top fractions. And get rid of the compound fraction. Unless you already know derivatives then we can actually skip this part.

2. muffin Group Title

so a common denominator for the top fractions? do i expand the (x+h)^2

3. myininaya Group Title

You will need to.

4. muffin Group Title

so x^2 + 2xh + h^2, what would be the common denominator

5. myininaya Group Title

x^2(x+h)^2

6. myininaya Group Title

|dw:1379983226588:dw|

7. myininaya Group Title

|dw:1379983241382:dw|

8. muffin Group Title

2xh + h^2/ x^2 (x+h)^2 x (1/h)

9. muffin Group Title

can i factor out a h from the numerator?

10. muffin Group Title

so i factored out an h from the numerator, than cancelled the h from 1/h

11. myininaya Group Title

What happen to your negative in from 2xh?

12. myininaya Group Title

h/h=1 yep yep

13. muffin Group Title

i have lim h--0 2x+h/ x^2(x+h)^2

14. muffin Group Title

so now i can "sub" in 0 into h, but what value goes for x?

15. myininaya Group Title

Well yeah but still you are missing a negative on top

16. myininaya Group Title

only h is going somewhere x stays

17. myininaya Group Title

It said what happens as h goes to zero (it said nothing for x)

18. myininaya Group Title

Did you figure out what negative you are missing?

19. muffin Group Title

ok i think i see my mistake so i went thru the stages again and right now I have lim h--0 -2x-h/x^2 (x+h)^2

20. muffin Group Title

because I factored out an h, but im confused as to my next step

21. myininaya Group Title

h goes to 0

22. muffin Group Title

is my answer suppose to be just a number? or will it have a value and x

23. myininaya Group Title

24. muffin Group Title

-2x-0/x^2 (x+0) ^2 ?

25. myininaya Group Title

(-2x-0)/(x^2(x+0)^2) yes Simplify.

26. muffin Group Title

-2/x?

27. muffin Group Title

not rlly syre how to simplify the denominator

28. mathslover Group Title

$$\cfrac{(-2x-0)}{(x^2)(x+0)^2}$$ (Just for ease - wrote the LaTeX)

29. myininaya Group Title

-2x-0=-2x x^2(x+0)^2=x^2(x)^2 (since x+0=x) Use law of exponents.

30. myininaya Group Title

Recall one of the laws of exponents a^m * a^n=a^(m+n)

31. muffin Group Title

ok so my answer is -2/x^3

32. myininaya Group Title

yep

33. muffin Group Title

thank you :)

34. mathslover Group Title

But the denominator should be x^4 @myin

35. myininaya Group Title

-2x/x^4=-2/x^3

36. muffin Group Title

I have another question: find the limit if it exists limx-- -2 2-|x|/ 2+x

37. muffin Group Title

thats lim x approaches -2

38. muffin Group Title

can I just sub in -2 for x? so that makes it 0/0

39. mathslover Group Title

Oh sorry @myininaya - didn't saw that :) Thanks !

40. myininaya Group Title

$\lim_{x \rightarrow -2} \frac{2-|x|}{2+x}$ ?

41. muffin Group Title

yes

42. myininaya Group Title

So we can't just simply plug in -2 because our denominator will be 0. Is there someway to make the function continuous at x=-2 so we can just plug in Well |x|=x if x>=0 and -x if x<0 Since x approaches -2 then x is negative since we are looking at what surrounds a negative number so we have |x|=-x

43. myininaya Group Title