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S11_202Hhwk3 - ECE 202H Spring 2011 Questions that are...

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ECE 202H Spring 2011 Page 1 of 2 ECE 202H: Homework #3 Due: 3 February 2011 at 1:30 PM (5 Points) Questions that are marked with a circled asterisk are to be submitted at the beginning of class on the specified due date. All other problems are provided for practice and are representative of problems that may be included on exams. Solutions to all problems will be posted after the due date. SHOW ALL WORK! Foundational Mathematics 1. The Chain Rule for a function of two variables states that if 𝑥 = 𝑥 ( 𝑡 ) and 𝑦 = 𝑦 ( 𝑡 ) where 𝑥 and 𝑦 are differentiable at 𝑡 and also 𝑤 = 𝑓 ( 𝑥 , 𝑦 ) is differentiable at ( 𝑥 ( 𝑡 ), 𝑦 ( 𝑡 )) , then 𝑤 = 𝑓 ( 𝑥 ( 𝑡 ), 𝑦 ( 𝑡 )) is differentiable at 𝑡 and its derivative is given by 𝜕𝑤 𝜕𝑡 = 𝜕𝑤 𝜕𝑥 𝜕𝑥 𝜕𝑡 + 𝜕𝑤 𝜕𝑦 𝜕𝑦 𝜕𝑡 Suppose that 𝑧 ( 𝑡 ) is differentiable at 𝑡 and 𝑤 = 𝑓 (( 𝑥 ( 𝑡 ), 𝑦 ( 𝑡 ), 𝑧 ( 𝑡 )) is differentiable at ( 𝑥 ( 𝑡 ), 𝑦 ( 𝑡 ), 𝑧 ( 𝑡 )) . State the
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