Chapter Review Jeopardy(1) by hcj

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• pg 1
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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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