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

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

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

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

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

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

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

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

muffin
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1Well yeah but still you are missing a negative on top

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

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

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

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

muffin
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1Your answer will be a function of x.

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

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

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

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

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

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

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

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

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

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

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