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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You will need to.
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
so x^2 + 2xh + h^2, what would be the common denominator
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
x^2(x+h)^2
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1379983226588:dw
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1379983241382:dw
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
2xh + h^2/ x^2 (x+h)^2 x (1/h)
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
can i factor out a h from the numerator?
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
so i factored out an h from the numerator, than cancelled the h from 1/h
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
What happen to your negative in from 2xh?
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
h/h=1 yep yep
 11 months ago

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Well yeah but still you are missing a negative on top
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
only h is going somewhere x stays
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
It said what happens as h goes to zero (it said nothing for x)
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Did you figure out what negative you are missing?
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
ok 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
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
because I factored out an h, but im confused as to my next step
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
h goes to 0
 11 months ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Your answer will be a function of x.
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
2x0/x^2 (x+0) ^2 ?
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
(2x0)/(x^2(x+0)^2) yes Simplify.
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
not rlly syre how to simplify the denominator
 11 months ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
2x0=2x x^2(x+0)^2=x^2(x)^2 (since x+0=x) Use law of exponents.
 11 months ago

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

muffin Group TitleBest ResponseYou've already chosen the best response.0
ok so my answer is 2/x^3
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
thank you :)
 11 months ago

mathslover Group TitleBest ResponseYou've already chosen the best response.0
But the denominator should be x^4 @myin
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
2x/x^4=2/x^3
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
I have another question: find the limit if it exists limx 2 2x/ 2+x
 11 months ago

muffin Group TitleBest ResponseYou've already chosen the best response.0
thats lim x approaches 2
 11 months ago

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

mathslover Group TitleBest ResponseYou've already chosen the best response.0
Oh sorry @myininaya  didn't saw that :) Thanks !
 11 months ago

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
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
 11 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
That is your key ingredient
 11 months ago
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