Chapter 1: Q18E (page 34)
Use a table of values to estimate the value of the limit.
\(\mathop {lim}\limits_{x \to 0} \frac{{{9^x} - {5^x}}}{x}\)
The value of limit \(\mathop {\lim }\limits_{x \to 0} \frac{{{9^x} - {5^x}}}{x}\)is 0.58.
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Find the domain and sketch the graph of the functions\({\bf{f}}\left( {\bf{x}} \right){\bf{ = }}\left\{ \begin{array}{l}{\bf{3 - }}\frac{{\bf{1}}}{{\bf{2}}}{\bf{x}},{\bf{x}} \le {\bf{2}}\\{\bf{2x - 5}},{\bf{x}} > {\bf{2}}\end{array} \right.\).
Find
(a) \({\bf{f + g}}\)
(b) \({\bf{f}} - {\bf{g}}\)
(c) \({\bf{fg}}\)
(d) \({\bf{f}}/{\bf{g}}\)
and state their domains.
38. \({\bf{f}}\left( x \right) = \sqrt {3 - x} \) \(g\left( x \right) = \sqrt {{x^2} - 1} \)
Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
\(y = \left| x \right| - 2\)
Prove the statement using the \(\varepsilon \) \(\delta \)definition of a limit.
\(\mathop {\lim }\limits_{x \to - 1.5} \frac{{9 - 4{x^2}}}{{3 + 2x}} = 6\)
An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If trepresents the time in minutes since the plane has left the terminal, let \(x\left( t \right)\)be the horizontal distance traveled and \(y\left( t \right)\) be the altitude of the plane.
(a) Sketch a possible graph of\(x\left( t \right)\).
(b) Sketch a possible graph of\(y\left( t \right)\).
(c) Sketch a possible graph of the ground speed.
(d) Sketch a possible graph of the vertical velocity.
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