problem_set_6 - Name Section Student ID Last First MI Math...

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1 Name: First MI Last Student ID # Problem Set #6 Score Section: C REDIT 2 1 0 Problem #1 . Evaluate lim ( x , y ) (0, 0) f ( x , y ) – or show that the limit does not exist – where f ( x , y ) = x 2 2 x 4 y 4 y 2 x 2 y 2 . C REDIT 2 1 0 Problem #2 . Consider the function f ( x , y ) given by f ( x , y ) = x 2 y y 2 + x 4 . Show that the limit as x , y 0,0 of this function does not exist. In particular, show that all straight–line approaches to the origin yield zero but that other approaches give different answers. Math 32A Lecture #5 Fall 2007
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2 Problem Set #6 C REDIT 2 1 0 Problem #3 . Evaluate lim ( x , y ) (0, 0) f ( x , y ) – or show that the limit does not exist – where f ( x , y ) = sin xy xy . C REDIT 2 1 0 Problem #4 . Let f ( x , y ) = ax 2 by 2 x 2 y 2 . Under what conditions (on a and b ) does lim ( x , y ) (0, 0) f ( x , y ) exist? Show the complete derivation.
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3 Problem Set #6 C REDIT 2 1 0 Problem #5 . For any θ with 0 ≤ θ ≤ 2 π , show that |cos θ | + |sin θ | ≥ 1. C REDIT 2 1 0 Problem #6 .
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