- #1
HerpMcDerp
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Homework Statement
[12] 3.Thetemperature T(x, y) at a point of the xy-plane is given by
T(x,y)= ye^(x^2).
A bug travels from left to right along the curve y = x^2
at a speed of 0.01m/sec. The bug
monitors T(x, y) continuously. What is the rate of change of T as the bug passes through
the point (1, 1)?
Homework Equations
Parameterizing x and y in terms of t, taking into account the velocity given (and assuming x and y are in meters, t is in seconds):
x = 0.01t
y = (0.01t)^2
t = 100 s
Chain rule
dT/dt = Tx dx/dt + Ty dy/dt
The Attempt at a Solution
dT/dt = 2xye^(x^2) * 0.01 + e^(x^2) * 0.02(0.01t) = 2*1*1*e * 0.01 + 0.02*e * 1 =
0.04*e degrees/sec
Right? Lol.