Calculus 3 Timed Quiz 3

Definition (Limit of a Multivariate Function) Let be a real-valued function, then

_____

means that for each given number _____ , there exists a number _____ so that if is a point in the ______________ of then

Definition (Continuity of Multivariate Functions) The function is continuous at the point if

        (i) is in the _________________ of ,
    
        (ii) exists, and
    
        (iii) ___________________ .

Definition (Partial Derivative of a Multivariate Function) If is a function of the _____________ ,  then the ____________   _____________ of with respect to _____ is the function defined by

.

Proposition (Clairaut's Theorem) If the function has mixed _________________ partial derivatives and , that are __________________ on an open disk containing , then ________________.

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Calculus 3 Timed Quiz 3
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/calculus-3-timed-quiz-3.html