Math 1320 Lab 10
Name:
1. Suppose that the celsius temperature of a hot plate is modeled by the following function.
2 +y 2 )
T (x, y) = 150e−(3x
Accurately draw a typical level curve of T (x, y). What is a physical interpretation of
the level curves?
2. Use polar coordinates to find the value of the following limit.
sin(3x2 + 3y 2 )
(x,y)→(0,0)
x2 + y 2
lim
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3. Consider the following series.
F (x, y) = −
∞
X
(y 2 − x3 − 16)n
n=1
n
Within the region of convergence of the above series, find explicit formulas for the partial
derivatives Fx and Fy (your answers should not be series). Hint: Consider the variable
substitution s = y 2 − x3 − 16.
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4. Find a parametrization of the torus given by the following equation.
2
p
4 − x2 + y 2 + z 2 = 1
It may be useful to see the surface plot of the above equation:
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