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practice_final - Here are some problems from an old final...

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Here are some problems from an old final exam for you to practice with. The material is covered quite differently year to year, so some of these problems may not be applicable (especially the qualitative ones listed below). They are provided for your convenience in understanding how I will be testing on the material from the last unit. 1. (5 points) List three uses of nanoparticles in nanobiotechnology. 2. (5 points) What is a quantum dot? 3. ( 5 points) What is electrophoresis?
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4. Does the integral of df from (x 1 , y 1 ) to (x 2 , y 2 ) depend on the path you take from the initial to the final point if df=3x 2 dx+ 14y 4 dy? Why or why not?
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5. Find the extremum of the function f(x,y) = 4x 2 + 4y 2 , subject to the constraint that x+y=4. Is this point a maximum, minimum or saddle point? Explain your answer.
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