Kevin Le
–
Math 226 SI
wwwscf.usc.edu/~kevinle, www.usc.edu/si
[email protected]
Week 5
§§11.211.5: Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximations, Chain Rule
§11.2: Limits and Continuity
1. Find the limit if it exists, or show that the limit does not exist.
a)
(
)
(
)
b)
(
)
(
)
2. Determine the set of points at which the function
(
)
√
is continuous.
§11.3: Partial Derivatives
3. Clairaut
’
s Theorem states that if a function
( )
has continuous second partial derivatives at any given
point, then
.
Verify that the conclusion of Clairaut
’
s Theorem holds for
.
4. Laplace
’
s Equation can be written as
.
Determine whether the function
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 '07
 KAMIENNY
 Math, Calculus, Continuity, Approximation, Chain Rule, Derivative, Linear Approximation, Limits, Laplace, Tangent Planes, Kevin Le, [email protected]

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