hw10-4 - -√ 7 √ 3 P 5 From the Online Textbook Section...

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Math 170-010 Homework 10/4 Fall 2011 Goals: Learn new vocabulary: normal slope and normal line . Compute implicit derivatives. Compute tangent and normal slopes at specifc points. Exercises: 1. From the Online Textbook, Section 4.9: Problems 2, 4, 5 and 7. 2. Re±er to the Online Textbook, Section 4.9: Problem 1. (a) Compute the tangent slope at the point (2 , 5). (b) Compute the normal slope at the point ( 3 , - 2). 3. Re±er to the Online Textbook, Section 4.9: Problem 8. (a) Compute the tangent slope at the point (1 / 3 , 1 / 4). (b) Compute the normal slope at the point (1 / 10 , - 1 / 3). 4. Re±er to the Online Textbook, Section 4.9: Problem 2. (a) Compute the tangent and normal slopes at the point p 7 3 , - 2 7 3 P (b) Compute the tangent and normal slopes at the point p 2 7 3 ,
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Unformatted text preview: -√ 7 √ 3 P 5. From the Online Textbook, Section 4.9: Problem 14. Challenge Problem: Compute the angle between the tangent lines in the fgure below. The two curves are given by x 2 + 2 xy + 4 y 2 = 7 and 4 x 2 + 4( y + 1) 2 = 5 There are two answers. I want the one that is less than 90 ◦ . Exact is best, but a decimal answer is acceptable i± it is in radians and it is correct to three decimal places. 1 Hints and Answers Exercises: 2. (a) 2 / √ 5; (b) 2 / √ 3. 3. (a)-9 / 16; (b) 9 / 100. 4. (a) Tangent is horizontal, slope = 0. Normal is vertical, slope = ∞ . (b) Tangent is vertical, slope = ∞ . Normal is horizontal, slope = 0. Challenge: arctan 2 + arctan(1 / 10) ≈ 1 . 2068 radians. 2...
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hw10-4 - -√ 7 √ 3 P 5 From the Online Textbook Section...

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