Chapter 1: Q6E (page 7)
3-16 A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.
The function is one-to-one.
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Determine whether f is even, odd, or neither. You may wish to use a graphing calculator or computer to check your answer visually.
82. \(f\left( x \right) = \frac{{{x^{\bf{2}}}}}{{{x^{\bf{4}}} + {\bf{1}}}}\)
A student bought a smartwatch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded t minutes after 3.00 PM on the first day she wore the watch.
t(min) | 0 | 10 | 20 | 30 | 40 |
Steps | 3438 | 4559 | 5622 | 5622 | 7398 |
(a) Find the slopes of the secant lines corresponding to given intervals of t. What do these slopes represent?
(i) \(\left( {{\bf{0}},{\bf{40}}} \right)\) (ii) \(\left( {{\bf{10}},{\bf{20}}} \right)\) (iii) \(\left( {{\bf{20}},{\bf{30}}} \right)\)
(b) Estimate the student’s walking pace, in steps per minute, at 3:20 PM by averaging the slopes of two secant lines.
39-46 find the domain of the function.
45. \(F\left( p \right) = \sqrt {2 - \sqrt p } \)
Question:
(a) Approximate f by a Taylor polynomial with degree n at the number a.
(b) Use Taylor's Formula to estimate the accuracy of the approximation \[f(x) \approx {T_n}(x)\] when x lies in the given interval.
(c) Check your result in part (b) by graphing \[\left| {{{\rm{R}}_{\rm{n}}}{\rm{(x)}}} \right|\]
\[f(x) = \sin x,\;\;\;a = \frac{\pi }{6},\;\;\;n = 4,\;\;\;0 \le x \le \frac{\pi }{3}\]
Find the domain and sketch the graph of the function \(f\left( x \right) = \frac{{{x^2} - 4}}{{x - 2}}\).
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