Exam 2 Supplemental Problems Words of Advice Here are few things to keep in

Exam 2 supplemental problems words of advice here are

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Exam 2 Supplemental Problems Words of Advice Here are few things to keep in mind when taking your exam: Show all work! The thought process and your ability to show how and why you arrived at your answer is more important than the answer itself. The exam will be designed so that you can complete it without a calculator. If you find yourself yearning for a calculator, you might be doing something wrong. Make sure you have answered the question that you were asked. Also, ask yourself if your answer makes sense. If you know you made a mistake, but you can’t find it, explain why you think you made a mistake and indicate where the mistake might be. This shows that you have a good understanding of the problem. If you write down an “=” sign, then you better be sure that the two expressions on either side are equal. Similarly, if two things are equal and it is necessary that they be equal to make your conclusion, then you better use “=.” Don’t forget to write limits where they are needed. Derivative Practice Find the derivative of each of the following functions. 1. f ( x ) = π 2 2. f ( t ) = 3 e 4 t 3. g ( w ) = e 3 3 w 4. h ( s ) = e 2 s ln(2 s ) 5. f ( x ) = 5 p log 3 ( x ) 6. g ( x ) = x 2 e x 2 7. f ( x ) = x e 8. f ( x ) = ( πe ) 2 9. m ( t ) = tan(3 t ) 10. g ( y ) = y cos(ln( y ))) 11. h ( t ) = t sin( t ) 12. f ( x ) = x sin( x ) 13. f ( x ) = ln x 3 / 5 3 - x ( x 2 - 4) 4 ! 14. y = x cos( x ) . 15. f ( x ) = e x 2 cos (2 x ) 3 x + 1 Derivatives in Multiple Ways Find the derivative of each of the following functions in at least two different ways. 16. f ( x ) = ( x + 1)( x 2 - 3) 17. g ( x ) = 3 x 2 + 5 x x 18. y = x 2 - 1 x 19. f ( x ) = 7 x + 3 x 2 5 x 20. a ( t ) = 2 sin 2 ( t ) + 2 cos 2 ( t ) 21. m ( v ) = arccos(cos( v ))
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MAT 136: Calculus I Exam 2 Supplemental Problems Implicit Differentiation Use implicit differentiation to calculate dy dx for the following implicitly defined functions. 22. xy = 1 + x 2 y 23. cos( x - y ) = y sin( x ) 24. x 3 + x 2 y + 4 y 2 = 6 25. x 2 sin( y ) = ln( xy ) Logarithmic Differentiation 26. Use logarithmic differentiation to show that d dx [ x x ] = x x (ln( x ) + 1) 27. Use logarithmic differentiation to find the derivative of f ( x ) = ( x + 2) 2 e 100+ x 3 sin 7 ( x ) . Proofs 28. Prove the Product Rule using the limit definition of the derivative. 29. Prove that d dx [sin( x )] = cos( x ) using the limit definition of the derivative.
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