021.09f.final

# 021.09f.final - HKUST MATH021 Concise Calculus Final...

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HKUST MATH021 Concise Calculus Final Examination Name: 17 th Dec 2009 Student I.D.: Tutorial Section: Seat Number: Directions: DO NOT open the exam until instructed to do so. You may write on both sides of the examination papers. You must show the steps in order to receive full credits. Electronic calculators are not allowed. Question No. Points Out of 1 3 2 4 3 4 4 4 5 10 6 10 7 10 8 10 9 10 10 10 1

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Some formula: sin( 𝑥 + 𝑦 ) = sin 𝑥 cos 𝑦 + cos 𝑥 sin 𝑦 sin( 𝑥 𝑦 ) = sin 𝑥 cos 𝑦 cos 𝑥 sin 𝑦 cos( 𝑥 + 𝑦 ) = cos 𝑥 cos 𝑦 sin 𝑥 sin 𝑦 cos( 𝑥 𝑦 ) = cos 𝑥 cos 𝑦 + sin 𝑥 sin 𝑦 tan( 𝑥 + 𝑦 ) = tan 𝑥 +tan 𝑦 1 tan 𝑥 tan 𝑦 tan( 𝑥 𝑦 ) = tan 𝑥 tan 𝑦 1+tan 𝑥 tan 𝑦 sin 2 𝑥 = 2 sin 𝑥 cos 𝑥 cos 2 𝑥 = cos 2 𝑥 sin 2 𝑥 = 2 cos 2 𝑥 1 = 1 2 sin 2 𝑥 2
1. (a) What is an even function?

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