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University of Texas at Dallas Assignment #5 Last Name: First Name and Initial: Course Name: Number: Mathematical Analysis 1 MATH 4301 Instructor: Due...

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University of Texas at Dallas Assignment #5 Last Name: First Name and Initial: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Course Name: Number: Mathematical Analysis 1 MATH 4301 Instructor: Due Date: Wieslaw Krawcewicz November 26, 2012 E-mail Address: Student’s Signature: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Instructions: 1. Print this booklet 2. Use the space provided to write your solutions in this booklet 3. Hand in your assignment to your instructor on the due date during the class time. Question Weight Your Score Comments 1. 10 2. 10 3. 10 4. 10 5. 10 Total: 100 2
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Let f (x, y ) = x2 + y 2 − 1+x2 and g (x, y ) = x + y , then we see that we see
that
A = f −1 ((−∞, 0]) ∩ g −1 ([0, ∞)) As f and g are continuous, hence f −1 ((−∞, 0]) and g...

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