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muffin
 one year ago
Evaluate the limit, if it exists
lim h0 ((1/(x+h)^2  1/x^2 ))/ h
muffin
 one year ago
Evaluate the limit, if it exists lim h0 ((1/(x+h)^2  1/x^2 ))/ h

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myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Try combining top fractions. And get rid of the compound fraction. Unless you already know derivatives then we can actually skip this part.

muffin
 one year ago
Best ResponseYou've already chosen the best response.0so a common denominator for the top fractions? do i expand the (x+h)^2

muffin
 one year ago
Best ResponseYou've already chosen the best response.0so x^2 + 2xh + h^2, what would be the common denominator

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1dw:1379983226588:dw

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1dw:1379983241382:dw

muffin
 one year ago
Best ResponseYou've already chosen the best response.02xh + h^2/ x^2 (x+h)^2 x (1/h)

muffin
 one year ago
Best ResponseYou've already chosen the best response.0can i factor out a h from the numerator?

muffin
 one year ago
Best ResponseYou've already chosen the best response.0so i factored out an h from the numerator, than cancelled the h from 1/h

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1What happen to your negative in from 2xh?

muffin
 one year ago
Best ResponseYou've already chosen the best response.0i have lim h0 2x+h/ x^2(x+h)^2

muffin
 one year ago
Best ResponseYou've already chosen the best response.0so now i can "sub" in 0 into h, but what value goes for x?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Well yeah but still you are missing a negative on top

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1only h is going somewhere x stays

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1It said what happens as h goes to zero (it said nothing for x)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Did you figure out what negative you are missing?

muffin
 one year ago
Best ResponseYou've already chosen the best response.0ok i think i see my mistake so i went thru the stages again and right now I have lim h0 2xh/x^2 (x+h)^2

muffin
 one year ago
Best ResponseYou've already chosen the best response.0because I factored out an h, but im confused as to my next step

muffin
 one year ago
Best ResponseYou've already chosen the best response.0is my answer suppose to be just a number? or will it have a value and x

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Your answer will be a function of x.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1(2x0)/(x^2(x+0)^2) yes Simplify.

muffin
 one year ago
Best ResponseYou've already chosen the best response.0not rlly syre how to simplify the denominator

mathslover
 one year ago
Best ResponseYou've already chosen the best response.0\(\cfrac{(2x0)}{(x^2)(x+0)^2}\) (Just for ease  wrote the LaTeX)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.12x0=2x x^2(x+0)^2=x^2(x)^2 (since x+0=x) Use law of exponents.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Recall one of the laws of exponents a^m * a^n=a^(m+n)

muffin
 one year ago
Best ResponseYou've already chosen the best response.0ok so my answer is 2/x^3

mathslover
 one year ago
Best ResponseYou've already chosen the best response.0But the denominator should be x^4 @myin

muffin
 one year ago
Best ResponseYou've already chosen the best response.0I have another question: find the limit if it exists limx 2 2x/ 2+x

muffin
 one year ago
Best ResponseYou've already chosen the best response.0thats lim x approaches 2

muffin
 one year ago
Best ResponseYou've already chosen the best response.0can I just sub in 2 for x? so that makes it 0/0

mathslover
 one year ago
Best ResponseYou've already chosen the best response.0Oh sorry @myininaya  didn't saw that :) Thanks !

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\lim_{x \rightarrow 2} \frac{2x}{2+x}\] ?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1So 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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1That is your key ingredient
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