anonymous
  • anonymous
Find the domain for the particular solution to the differential equation dy dx equals the quotient of negative 1 times x and y, with initial condition y(2) = 2.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
https://gyazo.com/6439d6ba1afb5baf216c9b05cf9296f0
anonymous
  • anonymous
@timo86m would you know?
anonymous
  • anonymous
sorry haven't taken DE yet

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anonymous
  • anonymous
It's cool. I appreciate you taking your time to read the question.
anonymous
  • anonymous
@freckles Would you happen to know?
freckles
  • freckles
first find when when dy/dx does not exist note dy/dx is -x/y and -x/y is fine unless ....?
freckles
  • freckles
think fractions are not cool if the bottom is ...
anonymous
  • anonymous
0
freckles
  • freckles
right we don't want y to be 0... now we need to keep this in mind after we solve the differential equation we will try to use this so what do you get when you solve dy/dx=-x/y
anonymous
  • anonymous
I got \[y = \sqrt{\frac{ -x^2 }{ 4 }+5}\]
freckles
  • freckles
not sure how you got the 5... \[y dy=-x dx \\ \frac{y^2}{2}=\frac{-x^2}{2}+C \\ \text{ I would \not attempt \to solve for } y \text{ yet } \\ \text{ but I'm going \to use the condition given \to find } C \\ \frac{2^2}{2}=\frac{-2^2}{2}+C \\ \frac{2(2)^2}{2}=C \\ C=2^2=4 \\ \frac{y^2}{2}=\frac{-x^2}{2}+4 \\ y^2=-x^2+8 \\ \text{ but } y \neq 0 \\ \text{ so } -x^2+8 \neq 0 \text{ when ? }\]
anonymous
  • anonymous
What are you asking exactly?
freckles
  • freckles
for what x is -x^2+8=0?
anonymous
  • anonymous
\[\sqrt{8}\]
freckles
  • freckles
or?
anonymous
  • anonymous
-\[\sqrt{8}\]
freckles
  • freckles
|dw:1449725022181:dw|
anonymous
  • anonymous
-2sqrt(2) to 2sqrt(2)
freckles
  • freckles
right
anonymous
  • anonymous
Thanks
anonymous
  • anonymous
Just to confirm
anonymous
  • anonymous
You found C then found x-intercept?
freckles
  • freckles
no remember dy/dx=-x/y , we couldn't have y is 0
freckles
  • freckles
by y is 0 when -x^2+8 is 0
anonymous
  • anonymous
Ohhh ok got it
freckles
  • freckles
since if y=0 is then y^2=0 and y^2=-x^2+8
anonymous
  • anonymous
Can you check over another?
freckles
  • freckles
maybe
anonymous
  • anonymous
They quick ones
anonymous
  • anonymous
https://gyazo.com/ba019252b62625bf2b352b7aa4b86315
freckles
  • freckles
well to find critical numbers what do you usually do?
anonymous
  • anonymous
set equal to 0
freckles
  • freckles
what do you set equal to 0?
anonymous
  • anonymous
When looking at a graph they correspond to min/max values
anonymous
  • anonymous
f'
freckles
  • freckles
ok f'(x)=0 aka the x-intercepts of f'
freckles
  • freckles
however
freckles
  • freckles
let's take f(x)=x^3 as an example f'(x)=3x^2 and 3x^2=0 when x=0 but is (0,f(0)) a max or min?
anonymous
  • anonymous
Min
freckles
  • freckles
whaT?!!!
freckles
  • freckles
|dw:1449725709459:dw|
anonymous
  • anonymous
Would it not be a parabola? Which unless reflected has a min
freckles
  • freckles
|dw:1449725732938:dw|
freckles
  • freckles
no f(x)=x^3 is not a parabola
anonymous
  • anonymous
Were we not talking about f'?
freckles
  • freckles
I wanted to find the max/min of f(x)=x^3
freckles
  • freckles
if they existed
freckles
  • freckles
f(x)=x^3 f'(x)=3x^2 3x^2=0 when x=0 but (0,f(0)) is neither a max or min
freckles
  • freckles
this example was suppose to show that it is not necessarily true that if f'(a)=0 then you have a min or max at x=a
anonymous
  • anonymous
And that is exactly why I chose D
freckles
  • freckles
you chose well
anonymous
  • anonymous
;)
freckles
  • freckles
but I'm confused why you would want to find the max or min of f'(x)
freckles
  • freckles
and not f(x)
anonymous
  • anonymous
I was confused by the way it was written.
freckles
  • freckles
hmmm... okay...
freckles
  • freckles
I don't know how else to write it sorry
freckles
  • freckles
the way I usually find the critical numbers of f(x)=x^3 or some other polynomial function is to find f'(x) and solve f'(x)=0 first
anonymous
  • anonymous
Isn't that what we all should do?
freckles
  • freckles
well the example was a polynomial... you should always consider f'(x)=0 even if it isn't a polynomial there are other functions where you have to consider when f'(x) does not exist
anonymous
  • anonymous
Got it.
anonymous
  • anonymous
I'd really appreciate it if you could help me with one last one that I am completely clue less on.
freckles
  • freckles
question 1: consider functions f(x)=1000 and g(x)=1 is one growing faster than the other? (look at graphs of the functions if you have to) question 2: consider function f(x)=0 and g(x)=1 is one growing faster than the other? (look at graphs) question 3: consider function f(x)=x^2 and g(x)=x? is one growing faster than the other? (look at graphs)
anonymous
  • anonymous
Q1: No Q2: No Q3: Yes But where is this coming from?
freckles
  • freckles
\[\lim_{x \rightarrow \infty} \frac{1000}{1}=1000 \\ \lim_{x \rightarrow \infty} \frac{0}{1}=0 \\ \lim_{x \rightarrow \infty}\frac{x^2}{x}=\infty\] they examples for each of the cases there
anonymous
  • anonymous
Oh, that wasn't the question.
freckles
  • freckles
what?
anonymous
  • anonymous
The last question I have, I created a new post for it
freckles
  • freckles
ok I don't see the question I only see question 7 but anyways good luck on the last question whatever it is I have to go peace

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