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mathcalculus
Group Title
HELP :( LINEARIZATION: Please use h in place of \Delta x and dx
I. If y= f(x)= 8 x^2+ 31 x + 12 find
a. dy =16xh+31
b. \Delta y = 8*(x+h)^2+31*(x+h)8x^231x
II. Evaluate each of these quantities if x=10 and h=0.04
a. dy= 37.4
b. \Delta y = 7.6528
 11 months ago
 11 months ago
mathcalculus Group Title
HELP :( LINEARIZATION: Please use h in place of \Delta x and dx I. If y= f(x)= 8 x^2+ 31 x + 12 find a. dy =16xh+31 b. \Delta y = 8*(x+h)^2+31*(x+h)8x^231x II. Evaluate each of these quantities if x=10 and h=0.04 a. dy= 37.4 b. \Delta y = 7.6528
 11 months ago
 11 months ago

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mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
why are my answers wrong? :(
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
for part a) you should have dy =16xh+31h
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
why have 31 h?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
if you start with y= x d (y = x) is dy = dx or using h instead of dx dy = h for your problem \[ d (y = 8 x^2+ 31 x + 12 )\\ dy = 8 dx^2 + 31 dx \\ dy = 16x dx +31 dx \\ dy = 16x \ h + 31 \ h \]
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
i thought we leave the constant alone?
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh because it was an x because finding the derivative?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
compared with \[ d (y = 31 x ) \\ dy = 31\ dx \]
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
yes it ='s to 1
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
\[ \frac{d}{dx} (y = 31 x) \\ \frac{d}{dx}y = 31 \frac{d}{dx}x\\ \frac{dy}{dx}= 31\frac{dx}{dx}\\ \frac{dy}{dx}= 31\cdot 1=31 \]
 11 months ago

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

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
but i was confused why i couldn't leave 31 alone
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
and why i had to add h in the end..
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
maybe a better way to think of it is \[ \Delta y = \frac{dy}{dx} \Delta x \] where dy/dx is the derivative of your function \[ \frac{dy}{dx}= 16x + 31\] and \[ \Delta y = \frac{dy}{dx} \Delta x =(16x + 31)\Delta x= (16x + 31)h \]
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh okay, got cha.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
what if it had like an x and a y inside
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
could i still apply this?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
it would be the same idea, but you use "partial derivatives"
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
ex: dy/dx
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
so (d/dx+dy/dx)h ?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
do you have a specific question?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
it is a new topic to talk about functions of two variables f(x,y) = x^2 + y^2 for example you won't see those until calculus II
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
well i know that we have to do this: 2x*y(dy/dx) +2y*(d/dx).. right?
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
are you asking about f(x,y) = x^2 + y^2 or z = x^2 + y^2 ? we find the partial derivative with respect to x (that means treat y as a constant) fx (means partial derivative with respect to x) = 2x fy = 2y we then say \[ \Delta z = 2x \Delta x + 2y \Delta y \]
 11 months ago

phi Group TitleBest ResponseYou've already chosen the best response.1
But you won't see those type of problems.
 11 months ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.1
oh okay, thank you so much! :)
 11 months ago
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