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practice-quiz5

practice-quiz5 - 16 Find the equation of the tangent line...

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AMS 151 (Fall, 2009) Joe Mitchell Applied Calculus I Practice Problems for Quiz # 5 1. Let f ( x ) = 1 x 3 x +2 x . Find f ( x ). 2. Let f ( x ) = sin x cos x tan 5 x . Find f ( x ). 3. Let f ( x ) = e 3 x sin x cos x . Find f ( x ). 4. Let f ( x ) = (3 x 4 - 2 x 2 + 7) e 3 x . Find f ( x ) and f ′′ ( x ). 5. Let f ( x ) = (3 + x 9 · 15 x ) 22 . Find f ( x ). 6. Let g ( y ) = 7 (13 y +22) . Find g ( y ). 7. Let f ( x ) = r x + R x + x . Find f ( x ). 8. Suppose that h ( b ) = 2 ab + g ( b 2 ) and that g ( w ) = 3 w 2 . Find h ( b ), h ( a ), and h (2). 9. Let f ( x ) = e 3 x sin x cos x . Find f ( x ). 10. Let f ( x ) = 6 tan x +9 sec x . Find f ( x ). 11. Let h ( x ) = sin(2 x ). Find the 83rd derivative, h (83) ( x ). 12. Find the equation of the tangent line to the curve y = 3 cos x sin x at the point ( π/ 4 , 3 / 2). 13. Find the equation of the tangent line to the curve y = 2 sec x - 4 cos x at the point ( π/ 3 , 2). 14. Find the equation of the tangent line to the curve y = 2 ln( x ) at x = 5. 15. Find the equation of the tangent line to the curve xy 3 + xy = 2 at the point (1,1).
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Unformatted text preview: 16. Find the equation of the tangent line to the curve xy 3 + xy = 12 at the point (6,1). 17. The temperature, H , in degrees Fahrenheit, of a can of soda that is put into a refrigerator to cool is given as a function of time, t , in hours, by H ( t ) = 10 + 55 e − 2 t . Find the rate of change of the temperature of the soda in units of degrees Fahrenheit per minute. 18. Let f ( x ) = sin(cos(sin x )). Find f ′ ( x ). 19. Let f ( x ) = sin(cos( x 3 )). Find f ′ ( x ). 20. Let f ( x ) = 4 cos(6 ln(2 x )). Find f ′ ( x ). 21. Let f ( x ) = 7 log 9 ( ex ). Find f ′ ( x ). 22. Let f ( x ) = 3 x 3 x . Find f ′ ( x )....
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