Math Assistance?


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Question on number 6 [see attached], am I missing something or can someone please explain the separation of variables.

Question on number 8 [see attached], I know it is the limit definition, but what is the shortcut to solving it [/me doesn't remember].

Thanks in advance.

post-7-1072599579.jpg

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On Number 6, just find the derivative.

yeah you use derivative, but you can't solve for y by itself. you'll have to use dy/dx in place of derivative of y, without forgetting the "chain rule." crap i can't see image i'll post again...

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Question 6:

x^2 - 2xy + 4y^2 = 64

solution:

2x - [ (2x . dy/dx) + (y.2) ] + (8y . dy/dx) = 0

2x - 2x.dy/dx - 2y +8y.dy/dx =0

2x -2y + (8y-2x).dy/dx = 0

(8y-2x).dy/dx = 2y - 2x

dy/dx = (2y-2x)/(8y-2x)

I hope you can follow. By the way '.' stands for multiplicatioon

Question 8:

lim h app 0

[ 5 (1/2 + h)^4 - 5(1/2)^4 ]/h

Solution:

as h approaches 0, (1/2 + h)^4 approaches (1/2)^4

therefore the expression becomes:

[ 5(1/2)^4 - 5(1/2)^4 ]/h

now just look at the numerator, and ull see tht it works out to be 0

therefore the solution is tht as h approaches 0, the expression approaches 0 as well

lemme know if u need more help

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8. use l'hopital's:

20(.5+h)^3, h=0

20(.5)^3 = 20(1/8) = 5/2.

i think that's right.

hmmm

maybe my eyes are deceiving me

but didnt the original question posted up there have a power of 4 instead of 3 for (.5+h)

lemme check...

oh yes...my eyes are NOT deceiving me :no:

danish

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