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Chapter Review Jeopardy(1)

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Chapter Review Jeopardy(1) Powered By Docstoc
					1
 Inverse     Review of   Exponential   Logarithmic   Inverse Trig
Functions   Logarithms    Functions     Functions     Functions



  100         100           100           100           100

  200         200           200           200           200

  300         300           300           300           300

  400         400           400           400           400

  500         500           500           500           500
                                                                2
            Inverse Functions
                   100
• Find the inverse of the function.

           f (x) 14  7x          3




                                       3
                 Inverse Functions
                        200
     • Find the inverse of the function.
                        3x 1
                 g(x) 
                        x4



                                         4
              Inverse Functions
                     300
• Find the inverse of the function.

           y  x  4, x  0
                     2




                                      5
                Inverse Functions
                       400

• Suppose g is the inverse of f and f(2) = 7 and
         3                                       1
  f   . Find g
     (2)            (7). Use ( f ) 
                                  1
                                     (a)         1    .
         2                                 f  f (a))
                                              (



                



                                                           6
                Inverse Functions
                       500
                                    1
• If f(x) = 2x + cos(x), find ( f        )
                                           (1).
           1              1
  Use ( f ) 
            (a)            1        .
                      f  f (a))
                         (
                 




                                                  7
                Review of Logarithms
                        100
• Simplify the expressions.
  (a) log 311
            3

  (b)   log5 7
        5
  (c) log1025 + log104

  (d) log6360 – log610

                                       8
              Review of Logarithms
                      200
• Evaluate the following using a calculator and the
  change of base formula.
  1. log46

  2. log917




                                                  9
             Review of Logarithms
                     300
• A log table says that log 2 = 0.3010300 and log 9 =
  0.9542425. Describe how to find log 18 and log29 and
  compute both.




                                                         10
              Review of Logarithms
                      400
• Solve the exponential equations. Round to three
  decimal places, if necessary.

  (a)   10   9 x
                      100    x2

            3x  4        x 1
  (b)
        4            8
  (c)
        5   3x1
                      10
                       x 1
  (d)
        5   x1
                    3                              11
               Review of Logarithms
                       500
• Solve the following logarithmic equations. Round to
  three decimal places, if necessary.

(a)   log5 (x  4)  log5 (2x  8)
(b) log5125 – log55 = x

(c)   log 6 (2 x  1)  2
(d) ln(2x – 6) = 3


                                                        12
             Exponential Functions
                    100
• Compute the derivatives.

             sin 2 x
(a)   y e

                   ex
(b)   f (x)  e

                                     13
            Exponential Functions
                   200
(a) Find dy/dx if cos(x – y) = xex.




(a) Find the 1000th derivative of f(x) = xe-x.




                                                 14
           Exponential Functions
                  300
 • Find the equation of the tangent line to the
   curve 2e  x  y at the point (0,2).
             xy








                                              15
                     Exponential Functions
                            400
     • Find the integrals.
         3
     (a)  e 2x dx
           0


     (b)    (2  x)3   (2x)2
                                 dx

     (c)      3sin x cos xdx



                                            16
          Exponential Functions
                 500
• Find the equation of the tangent line to the
  graph of the function y = 3x-4 at (4,1).




                                             17
            Logarithmic Functions
                     100
• Find the derivative of each function.
  (a) y  2ln(x)  5ln(3x)




                     x 
  (b) f (x)  log 3        
                    2x  3 

                                          18
           Logarithmic Functions
                    200
• Find the equation of the tangent line to the
  function y = log3x at the point (27,3).




                                                 19
                    Logarithmic Functions
                             300
    • Integrate.
    (a)   5x  7x 2
                3    dx
              x
              x
    (b)  2       dx
          (x  5)
         2
    (c)   5   x
                   dx
         0



                                            20
            Logarithmic Functions
                     400
• Use logarithmic differentiation to find dy/dx.

                  y  (1  x)    1/ x




 
                                                   21
             Logarithmic Functions
                      500
• Use logarithmic differentiation to find the equation of the
  tangent line to the function y  (ln x)
                                            sin x

  at the point (e,1).



                 




                                                            22
                Inverse Trig Functions
                         100
• Evaluate the expressions without using a
  calculator.
         1
  (a) cos (1/2)

  (b)   arcsin(0)
                 1
  (c)   sin(cos ( 3 /2))
            
           1
           cos 
  (d) sin 
           6                             23
                  Inverse Trig Functions
                           200
     • Find the derivative of each function.
                    1
       (a) y  (sin x)
                         2




     (b) y  sin1(x 2 )




                                               24
                 Inverse Trig Functions
                          300
    • If f (x)  x tan1 x , find f 
                                     (1).



                      




                                            25
                   Inverse Trig Functions
                            400
     • Integrate.
             3
               6
       (a)       2 dx
           1 1 x



                  ex

       (b)   e   x2
                       1
                         dx




                                            26
                       Inverse Trig Functions
                                500
     • Integrate.

           3 /4
                    dx
     (a)
                 116 x 2
           0



                       2x
     (b)           e
                              dx
                  1e       4x




                                              27

				
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Jun Wang Jun Wang Dr
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