Thomas Calculus Early Transcendentals 15th Edition By Joel Hass, Christopher

Solutions Manual Thomas Calculus Early
Transcendentals 15th Edition By Joel Hass,
Christopher

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Solutions
Manual

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CHAPTER 1 FUNCTIONS

1.1 FUNCTIONS AND THEIR GRAPHS

1. domain  (, ); range  [1, ) 2. domain  [0, ); range  (, 1]

3. domain  [2, ); y in range and y  5 x  10  0  y can be any positive real number  range  [0, ).

4. domain  (, 0]  [3,  ); y in range and y  x 2  3x  0  y can be any positive real number 
range  [0, ).

5. domain  (, 3)  (3, ); y in range and y  4 , now if t  3  3  t  0  4  0, or if t  3 
3t 3t
3  t  0  3 4 t  0  y can be any nonzero real number  range  (, 0)  (0, ).


6. domain  (,  4)  ( 4, 4)  (4, ); y in range and y  2 , now if t  4  t 2  16  0  2  0, or if
t 2  16 t 2  16
4  t  4  16  t 2  16  0   16
2  2 2
, or if t  4  t  16  0  2  0  y can be any nonzero
t 2  16 t 2  16
real number  range  (,  18 ]  (0, ).

7. (a) Not the graph of a function of x since it fails the vertical line test.
(b) Is the graph of a function of x since any vertical line intersects the graph at most once.

8. (a) Not the graph of a function of x since it fails the vertical line test.
(b) Not the graph of a function of x since it fails the vertical line test.


9. base  x; (height)2   2x 
2
 x 2  height  2
3
x; area is a ( x)  1
2
(base)(height)  12 ( x)  x 
2
3
4
3 2
x ;
perimeter is p ( x)  x  x  x  3 x.

10. s  side length  s 2  s 2  d 2  s  d ; and area is a  s 2  a  12 d 2 .
2


11. Let D  diagonal length of a face of the cube and   the length of an edge. Then  2  D 2  d 2 and

 
2 2 3/2 3
D 2  2 2  3 2  d 2    d . The surface area is 6 2  6 d3  2d 2 and the volume is 3  d3  d .
3 3 3


 
12. The coordinates of P are x, x so the slope of the line joining P to the origin is m  xx  1 ( x  0).
x


Thus, x, x    1
m2
, 1
m .
13. 2 x  4 y  5  y   12 x  54 ; L  ( x  0)2  ( y  0)2  x 2  ( 12 x  54 )2  x 2  14 x 2  54 x  16
25

5 x2 5 25  20 x 2  20 x  25 20 x 2  20 x  25
 4
 4
x  16 16
 4


14. y  x  3  y 2  3  x; L  ( x  4) 2  ( y  0) 2  ( y 2  3  4)2  y 2  ( y 2  1)2  y 2
 y4  2 y2  1  y2  y4  y2  1

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2 Chapter 1 Functions

15. The domain is (, ). 16. The domain is (, ).




17. The domain is (, ). 18. The domain is (, 0].




19. The domain is (, 0)  (0, ). 20. The domain is (, 0)  (0, ).




21. The domain is 22. The range is [5, ) .
(, 5)  (5, 3]  [3, 5)  (5, ).

23. Neither graph passes the vertical line test.
(a) (b)