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 s2 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 g1 1 Use the functions f(x) x 4 and g(x) 2x 5 to find the given value. 87. g1 f 1