By Maurice D. Weir, Joel Hass, Christopher Heil, George B. Thomas Jr., Elka Block, Frank Purcell
This is often the instructor's suggestions handbook for Thomas' Calculus early transcendentals thirteenth version. It includes all of the solutions to either even and atypical questions in that publication. It additionally comprises the stairs had to arrive on the solutions.
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Additional resources for Single Variable: Thomas' Calculus Early Transcendentals (13th Edition) Instructor's Solutions Manual
6 Inverse Functions and Logarithms 31. Step 1: y Step 2: y x 3 x 2 y(x 2x 3 x 1 1 f 1 ( x); Domain of f 2x 3 x 1 2x 3 x 1 Domain of f f(f (2 x 3) 3( x 1) (2 x 3) 2( x 1) 2 y x 3 Step 2: y 1 3 x 32. Step 1: y 3x 2 x 1 1 2y = x + 3 x 3 x = 2y + 3 2y 3 y 1 x 2; y x 3y x x x x x 2 x and f 1 ( f ( x)) 5x 5 x xy y x 3 2 3 2 x 3 1 2( x 3) 3( x 2) ( x 3) ( x 2) 3y 5x 5 x 3y 2 y 1 x f 1 ( x); : ( (1, ), Range of f 1: [0, 9) , 0] 3x 2 x 1 ( x)) xy 1, Range of f 1: y : x f ( f 1 ( x )) 2) = x + 3 ; If x > 1 or x 3x 2 x 1 3x x 1 0 3 (9, ); 3x 2 x 1 0 3x 2 x 1 3x x 1 3x 3 x 1 3 3x 3 x 3( x 1) 3x 3 x and 2 x 3 f 1 ( f ( x)) 9x x 3 x x 1 x 3 33.
B) The logarithm attains all real values, so the range is ( , ). 28. (a) The function is defined for all values of x, so the domain is ( (b) The cube root attains all real values, so the range is ( , ). 29. (a) (b) (c) (d) , ). Increasing because volume increases as radius increases. Neither, since the greatest integer function is composed of horizontal (constant) line segments. Decreasing because as the height increases, the atmospheric pressure decreases. Increasing because the kinetic (motion) energy increases as the particles velocity increases.
11. 75 1 12. 91/3 91/6 35/3 32/3 16. 13 2 18. 3 19. 2 2 1 6 93 5 14. 75) 2 3 33 31 2 /2 1/2 1/2 24 1/ 2 4 (2 21. Domain: ( ) 161/4 2 3 13. 7 12 1/2 36 1/2 6 3 20. 5 254/8 17. 7 15. 25 2 (61/ 2 )2 32 6 9 2 3 . As x increases, e x becomes infinitely large and y becomes a smaller and smaller positive real number. As x decreases, e x becomes a smaller and smaller positive real number, y 1, 2 and y gets arbitrarily close to 12 22. Domain: ( 1 cos x 23. Domain: ( 24. If e2 x , ); y in range 1 y Range: 0, 12 .