Question
Asked Oct 30, 2019

I think this question (included in the image) is looking for a derivative of sorts

4t-4
cm and y 8+ Int cm, find the rate at which the temperature T changes when t
The temperature T= T(x.y) in °C at point (x.y) satisfies T,x(1,8) 2 and Ty(1,8)= -3. If x e'
1 sec.
C per sec.
When t 1 sec, the temperature changes at a rate of
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4t-4 cm and y 8+ Int cm, find the rate at which the temperature T changes when t The temperature T= T(x.y) in °C at point (x.y) satisfies T,x(1,8) 2 and Ty(1,8)= -3. If x e' 1 sec. C per sec. When t 1 sec, the temperature changes at a rate of

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Step 1

Please see the white board for the formulation.

ST dy
ST dx
Т -Та, у)
бу dt
бх dt
dt
dy
dx
dT
+ Tу
dt
dt
dt
dy
da
dT
+ Tу dt
dt
t=1 =
dt
t=1
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ST dy ST dx Т -Та, у) бу dt бх dt dt dy dx dT + Tу dt dt dt dy da dT + Tу dt dt t=1 = dt t=1

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Step 2

Please see the white board.

dax
4et-4
dt
t 1 e4x1-41
dx
4e4x1-4
dt
= 4
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dax 4et-4 dt t 1 e4x1-41 dx 4e4x1-4 dt = 4

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Step 3

y = 8+ ln t

Hence, dy/dt = 1/t

when t = 1, y = ...

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Tagged in

Math

Calculus