Chapter 1: Q43E (page 7)
39-46 find the domain of the function.
43. \(h\left( x \right) = \frac{1}{{\sqrt(4){{{x^2} - 5x}}}}\)
The domain of the function is \(\left( { - \infty ,0} \right) \cup \left( {5,\infty } \right)\).
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39-46 find the domain of the function.
46. \(h\left( x \right) = \sqrt {{x^2} - 4x - 5} \)
A tank hold 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaning in the tank (in gallons) after t minutes.
t(min) | 5 | 10 | 15 | 20 | 25 | 30 |
V(gal) | 694 | 444 | 250 | 111 | 28 | 0 |
(a) If P is the point (15, 250) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with \(t = {\bf{5}},\;{\bf{10}}{\rm{,}}\,{\bf{20}}{\rm{,}}\,{\bf{25}}{\rm{,}}\,{\bf{and}}\,\,{\bf{30}}\).
(b) Estimate the slope of the tangent line at P by averaging the slopes of two secant ines.
(c) Use a graph of V to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.)
If f and g are both even functions, is fg even? If f and g are both odd functions, is fg odd? What if f is even and g is odd? Justify your answers.
If \(g\left( x \right) = \frac{x}{{\sqrt {x + 1} }}\), find \(g\left( 0 \right)\), \(g\left( 3 \right)\), \(5g\left( a \right)\), \(\frac{1}{2}g\left( {4a} \right)\), \(g\left( {{a^2}} \right)\), \({\left( {g\left( a \right)} \right)^2}\), \(g\left( {a + h} \right)\), \(g\left( {x - a} \right)\).
If \(f\left( x \right) = 3{x^2} - x + 2\), find \(f\left( 2 \right)\), \(f\left( { - 2} \right)\), \(f\left( a \right)\), \(f\left( { - a} \right)\), \(f\left( {a + 1} \right)\), \(2f\left( a \right)\), \(f\left( {2a} \right)\), \(f\left( {{a^2}} \right)\), \({\left( {f\left( a \right)} \right)^2}\) and \(f\left( {a + h} \right)\).
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