BC Calculus
Sections 5.2/5.3
p. 338
Find the indefinite integral.
29.
cos 
 sin  d
35.

sec x tan x
dx
sec x  1
Find F’(x).
x
62. F(x)   tan t dt
0
Find the area of the given region. Use a graphing utility to verify your result.
4
67. y 
x
Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify your results.
71. y 
x2  4
, x  1, x  4, y  0
x
73. y  2sec
p. 347
Show that f and g are inverse functions (a) analytically and (b) graphically.
x 1
1. f(x)  5x  1
4. f(x)  1  x3
g(x) 
5
1
1
7. f(x) 
g(x) 
x
x
Given the graph of F(x) sketch the inverse G(x) on the same axis.
10.
x
, x  0, x  2, y  0
6
g(x)  3 1  x
Use a graphing utility to graph the function. Determine whether the function is one-to-one on its entire domain.
1
17. h  s  
19. f  x   ln x
3
s2
Find the inverse function of f. Graph f and f-1. Describe the relationship between the graphs.
34. f(x)  x2, x  0
Use the graph of the function f to complete the table and sketch the graph of f-1.
43.
x
f-1(x)
Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval.
4
2
47. f(x)   x  4  , [4, )
49. f(x)  2 , (0, )
x
Delete part of the domain so that the function that remains is one-to-one. Find the inverse function of the remaining
function and give the domain of the inverse function. (Note: There is more than one correct answer)
64. f(x)  16  x4
Find dy/dx at the given point for the equation.


82. x  2ln y 2  3 ,  0,4 
Use the functions f(x) 
83.
f
1

1
x  3 and g(x)  x 3 to find the given value.
8
g1 1
Use the functions f(x)  x  4 and g(x)  2x  5 to find the given value.
87. g1 f 1