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Exam2 MTH251 Practice with key

Exam2 MTH251 Practice with key - Exam 2 Practice Problems...

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Exam 2 Practice Problems MTH251 For questions 1 –6: Use differentiation rules to determine each of the following 1. 1 2 3 ) ( 3 5 - + - = x x x x f 2. ( 1 ) ( 2 + = x e x h x 3. 3 4 4 x x y + = 4. ( x x x f cos ln 2 ) ( - = 5. ) ln( ) ( 2 x x f = 6. x x x P tan ) ( = 7. Show that ( x x x dx d 3 3 3 1 cos sin sin = - . 8. Use implicit differentiation to find dx dy given ) sin( 2 x y y = . Note: Your final answer may contain both x’s and y’s. 9. Use implicit differentiation and the natural log function to differentiate 4 ) 1 ( cos + = x x e y x then find the equation of the tangent line when x = 0. Hint: take ln of both sides then differentiate. For questions 10 - 13, consider 3 3 2 ) ( x e x f x - = 10. Find ) ( x f . 11. Find ) ( x f . 12. At x = 1, is f increasing, decreasing, or neither? How do you know? 13. At x = 1 is the rate of change of f increasing, decreasing, or neither? How do you know? 14. Consider the function 8 4 ) ( 2 + - = x x x f . Find the equation of the line tangent to f at the point (3,5). For questions 13 and 14, a ball is thrown upward from a bridge that is 160 ft above the canyon floor. The ball’s height above the canyon floor is given by 0 ; 16 48 160 ) ( 2 - + = t t t t s , where s is measured in feet and t is in seconds. 15. What is the velocity of the ball at time t = 2 sec.? Is the ball still climbing or has it started its descent?

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Exam2 MTH251 Practice with key - Exam 2 Practice Problems...

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