MA1505_08S2_Test_Outline_Solutions[1]

MA1505_08S2_Test_Outline_Solutions[1] - MA 1505 Mathematics...

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Unformatted text preview: MA 1505 Mathematics 1 2008/2009 Semester 2 Mid-term Test Outline Solutions Question 1. Routine key steps : dy dx = 4 x 3- 8 x 3 . At x = 1, the slope of the tangent is- 4. Equation of the tangent is y = 9- 4 x . The y-intercept is p = 9. Question 2. Similar to Tutorial 1, Question 4 ( c ): dy dx = dy dt dx dt = 1 + sin t cos t ⇒ d dt dy dx = ··· = 1 + sin t cos 2 t . Thus, d 2 y dx 2 = 1 + sin t cos 2 t dx dt = 1 + sin t cos 3 t . Question 3. If x denotes the length of the side of the rectangular area parallel to the road, then the total length of fence required is f ( x ) = x + 2 5 , 000 x = x + 10 , 000 x , where x > . Then f ( x ) = 1- 10 , 000 x 2 and f 00 ( x ) = 20 , 000 x 3 > . Now, for x > 0 we have f ( x ) = 0 ⇐⇒ x = 100 gives local (and absolute) minimum . Thus, f (100) = 200. MA1505 Mid-term Test Outline Solutions Question 4. Let y = x x- e 3 x . Then ln y = x ln x x- e 3 = ln x x- e 3 1 x ....
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This note was uploaded on 05/05/2009 for the course MA MA1505 taught by Professor Ma1505 during the Spring '09 term at National University of Juridical Sciences.

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MA1505_08S2_Test_Outline_Solutions[1] - MA 1505 Mathematics...

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