calculus 3

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fntre12345

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hello there is 5 problems in the file inserted below please do all of the hand writting showing all work thank you

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Calculus III Last Name: First Name: Quiz 3-8-2018 Complete work is required to receive credit. --------------------------------------------------------------------------------------------1. Graph at least 5 level curves for each of the following functions. a) 𝑧 = √𝑥 2 + 4𝑦 2 b) 𝑧 = cos(2𝑥 + 𝑦) 2. Evaluate the following limits. a) b) c) lim 𝑥𝑦 (𝑥,𝑦)→(0,0) 𝑥 2 +𝑦 2 √𝑥+𝑦−3 (𝑥,𝑦)→(4,5) 𝑥+𝑦−9 lim lim 𝑥 2 +𝑦 2 (𝑥,𝑦)→(0,0) 𝑥(𝑦 2 −1) 3. The volume of an ellipsoid with axes of length 2𝑎, 2𝑏, 𝑎𝑛𝑑 2𝑐 is 𝑉 = 𝑑𝑣 𝜋 𝑎𝑏𝑐. Find the percentage of the relative change % when 𝑎 increases 𝑣 by 2%, and 𝑏 decreases by 2.5%, and 𝑐 increases by 3%. 4. Find the total differential for 𝑓(𝑢, 𝑣) = 1 − 𝑡𝑎𝑛−1 (𝑢2 𝑣 + 𝑣 2 𝑢). 5. Find 𝐹𝑥𝑦𝑧 , 𝐹𝑦𝑥𝑧 , and 𝐹𝑧𝑥𝑦 for the given function. 𝐹(𝑥, 𝑦, 𝑧) = tan(𝑥𝑦𝑧)
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