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Worksheet_3

# Worksheet_3 - dependant variable with respect to its...

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Worksheet 3 Multi-variable Functions 1a) Find the limit. y x y x y x y x y x - - + - 2 2 lim ) 0 , 0 ( ) , ( 1b) Using the ε δ - definition of the limit, show that there exists a 0 δ such that for all x,y,z the following is true: δ < + + 2 2 2 z y x ε < - ) 0 , 0 , 0 ( ) , , ( f z y x f ) ( tan ) ( tan ) ( tan ) , , ( 2 2 2 z y x z y x f + + = 03 . 0 = ε 2) Given = y x dt t g y x f ) ( ) , ( . Find x f and y f . ( Hint: Fund. Thm of Calc. )

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3) Given x y x f y log ) , ( = . Find x f and y f . 4) Suppose ) , , ( r q p f w = and ) , , ( z s x g p = , ) , , ( z s x h q = , ) , , ( z s x m r = . a) What are the independent, intermediate, and dependant variable(s)? b) Using the chain rule, write the expression(s) for the partial derivative of the
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Unformatted text preview: dependant variable with respect to its independent variable(s). c) Draw the “tree” diagram relating the variables in (a) and the expression of the chain rule in (b). 5) Find the value of dx dy / at the pt. (1,2) assuming ) ( x g y = . (May want to use y x F F dx dy-= where ) , ( = y x F and ≠ y F at pt. of interest.) 7 ) , ( 2 2-+ + = = y xy x y x F...
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Worksheet_3 - dependant variable with respect to its...

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