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**Unformatted text preview: **Kevin Le – Math 226 SI
www-scf.usc.edu/~kevinle, www.usc.edu/si
kevinle@usc.edu
Week 5
§§11.2-11.5: 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 is a solution of Laplace’s equation. Kevin Le – Math 226 SI
www-scf.usc.edu/~kevinle, www.usc.edu/si
kevinle@usc.edu
Week 5
§§11.2-11.5: Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximations, Chain Rule §11.4: Tangent Planes and Linear Approximations
5. Find an equation for the plane tangent to 6. Find the linear approximation of ( ) ( ) at the point ( ( ) at ( ). ) and use it to approximate ( 7. You measure a cone to have a height
and a radius
Estimate the largest error in the calculated volume. but with an error of §11.5: The Chain Rule
8. Determine and , where 9. Determine and , where , ( ). , and . ). . ...

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