121616949-math.307 - 293 Appendix B Selected Answers 4.7.4...

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Appendix B Selected Answers 293 4.7.4. e x cos( e x ) 4.7.5. cos( x ) e sin x 4.7.6. x sin x cos x ln x + sin x x 4.7.7. 3 x 2 e x + x 3 e x 4.7.8. 1 + 2 x ln(2) 4.7.9. - 2 x ln(3)(1 / 3) x 2 4.7.10. e 4 x (4 x - 1) /x 2 4.7.11. (3 x 2 + 3) / ( x 3 + 3 x ) 4.7.12. - tan( x ) 4.7.13. (1 - ln( x 2 )) / ( x 2 p ln( x 2 )) 4.7.14. sec( x ) 4.7.15. x sin( x ) (cos( x ) ln( x ) + sin( x ) /x ) 4.7.20. e 4.8.1. 0 4.8.2. 4.8.3. 1 4.8.4. 0 4.8.5. 0 4.8.7. y = 1 and y = - 1 4.9.1. x/y 4.9.2. - (2 x + y ) / ( x + 2 y ) 4.9.3. - (3 x 2 + y 2 - 2 xy ) / (2 xy - 3 y 2 - x 2 ) 4.9.4. sin( x ) sin( y ) / (cos( x ) cos( y )) 4.9.5. - y/ x 4.9.6. ( y sec 2 ( x/y ) - y 2 ) / ( x sec 2 ( x/y )+ y 2 ) 4.9.7. ( y - cos( x + y )) / (cos( x + y ) - x ) 4.9.8. - y 2 /x 2 4.9.9. 1 4.9.11. y = 2 x ± 6 4.9.12. y = x/ 2 ± 3 4.9.13. ( 3 , 2 3), ( - 3 , - 2 3), (2 3 , 3), ( - 2 3 , - 3) 4.9.14. y = 7 x/ 3 - 8 / 3 4.9.15. y = ( - y 1 / 3 1 x + y 1 / 3 1 x 1 + x 1 / 3 1 y 1 ) /x 1 / 3 1 4.9.16. ( y - y 1 ) / ( x - x 1 ) = (2 x 3 1 + 2 x 1 y 2 1 - x 1 ) / (2 y 3 1 + 2 y 1 x 2 1 + y 1 ) 4.10.3. - 1 / (1 + x 2 ) 4.10.4. 2 x 1 - x 4 4.10.5. e x 1 + e 2 x 5.1.1. min at x = 1 / 2 5.1.2. min at x = - 1, max at
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Unformatted text preview: max at x = 2, min at x = 4 5.1.4. min at x = ± 1, max at x = 0. 5.1.5. min at x = 1 5.1.6. none 5.1.7. none 5.1.8. min at x = 7 π/ 12 + kπ , max at x =-π/ 12 + kπ , for integer k . 5.1.9. none 5.1.10. local max at x = 5 5.1.11. local min at x = 49 5.1.12. local min at x = 0 5.1.15. one 5.2.1. min at x = 1 / 2 5.2.2. min at x =-1, max at x = 1 5.2.3. max at x = 2, min at x = 4 5.2.4. min at x = ± 1, max at x = 0. 5.2.5. min at x = 1 5.2.6. none 5.2.7. none...
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