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SOLUTIONS MANUAL CALCULUS EARLY TRANSCENDENTALS THIRD EDITION by William Briggs Lyle Cochran Bernhard Gillett - (All Chapters) Latest 2024 $12.99
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INSTRUCTOR’S SOLUTIONS MANUAL CALCULUS
EARLY TRANSCENDENTALS
THIRD EDITION by William Briggs Lyle Cochran Bernhard Gillett
Chapter 1
Functions
1.1 Review of Functions
1.1.1 A function is a rule that assigns each to each value of the independent variable
in the domain a unique value of the dependent variable in the range.
1.1.2 The independent variable belongs to the domain, while the dependent variable
belongs to the range.
1.1.3 Graph A does not represent a function, while graph B does. Note that graph
A fails the vertical line test, while graph B passes it.
1.1.4 The domain of f is [1, 4), while the range of f is (1, 5]. Note that the domain is
the “shadow” of the graph on the x-axis, while the range is the “shadow” of the
graph on the y-axis.
1.1.5 Item i. is true while item ii. isn’t necessarily true. In the definition of
function, item i. is stipulated. However, item ii. need not be true – for example, the
function f (x) = x2 has two different domain values associated with the one range
value 4, because f (2) = f (−2) = 4.
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1.1.1 The independent variable t is elapsed time and the dependent variable d is distance
above the ground. The domain in context is [0, 8]
1.1.2 The independent variable h is the height of the water in the tank and the
dependent variable V is the volume of water in the tank. The domain in context is
[0, 50]
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1.1.20 The graph would be the result of leaving the portion of the graph in the first quadrant, and
then also obtaining a portion in the third quadrant which would be the result of reflecting the
portion in the first quadrant around the y-axis and then the x-axis.
1.1.21 Function A is symmetric about the y-axis, so is even. Function B is symmetric about the
origin so is odd. Function C is symmetric about the y-axis, so is even.
1.1.22 Function A is symmetric about the y-axis, so is even. Function B is symmetric about the
origin, so is odd. Function C is also symmetric about the origin, so is odd.
1.1.26 Because the cube root function is defined for all real numbrs, the domain is R, the set of
all real numbers.
1.1.27 The domain consists of the set of numbers w for which 2 − w ≥ 0, so the interval (−∞, 2].
1.1.28 The domain consists of the set of numbers x for which 9 − x2 ≥ 0, so the interval [−3, 3].
1.1.29 Because 1 + t2 is never zero for any real numbered value of t, the domain of this function is
R, the set of all real numbers.
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