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265Lesson07Problems - general idea is that if you can Fnd...

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MATH 265: MULTIVARIABLE CALCULUS: LESSON 7 PROBLEMS Problems are worth 20 points each. (1) Sketch the graph of f ( x,y ) = x + y 2 . (2) Sketch the graph of f ( x,y ) = radicalbig 4 - x 2 - y 2 . (3) Thinking about the shape of the graph (no calulus needed), what is the largest value of f ( x,y ) = 1 1 + x 2 + y 4 ? (4) Evaluate lim ( x,y ) (1 , 2) e ( x - y ) 2 . (5) Evaluate lim ( x,y ) (0 , 0) sin x cos parenleftbigg 1 y parenrightbigg . Hint: study example 6, page 789, method 1. (6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Show lim ( x,y
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Unformatted text preview: general idea is that if you can Fnd two paths heading for ( a, b ) such that the limit of f ( x, y ) at ( a, b ) along the paths give two dierent results, then you can conclude lim ( x,y ) ( a,b ) f ( x, y ) does not exist. So, for this problem, you need to come up with two paths heading towards (0 , 0) along which x ( y + 1) y has two dierent limits. 1...
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