Chapter 1: Q39E (page 35)
Prove the statement using the\(\varepsilon \), \(\delta \)definition of a limit.
\(\mathop {\lim }\limits_{x \to 0} {x^2} = 0\)
It is proved that\(\mathop {\lim }\limits_{x \to 0} {x^2} = 0\).
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The graph shows the height of the water in a bathtub as a function of time. Give a verbal description of what you think happened.
Express the surface area of a cube as a function of its volume.
Use the table to evaluate each expression.
(a) \(f\left( {g\left( 2 \right)} \right)\) (b) \(g\left( {f\left( 0 \right)} \right)\) (c) \(f \circ g\left( 0 \right)\) (d) \(g \circ f\left( 6 \right)\) (e) \(g \circ g\left( { - 2} \right)\) (f) \(f \circ f\left( 4 \right)\)
The graph of\({\bf{f}}\)is given. Draw the graphs of the following functions.
(a)\({\bf{y = f}}\left( {\bf{x}} \right){\bf{ - 2}}\)
(b)\({\bf{y = f}}\left( {{\bf{x - 2}}} \right)\)\(\)
(c)\({\bf{y = - 2f}}\left( {\bf{x}} \right)\)
(d)\({\bf{y = f}}\left( {\frac{{\bf{1}}}{{\bf{3}}}{\bf{x}}} \right){\bf{ + 1}}\)
Find the functions (a)\({\bf{f}} \circ {\bf{g}}\), (b)\({\bf{g}} \circ {\bf{f}}\), (c)\({\bf{f}} \circ {\bf{f}}\), and (d) \({\bf{g}} \circ {\bf{g}}\) and their domains.
\({\bf{f}}\left( {\bf{x}} \right){\bf{ = x + }}\frac{{\bf{1}}}{{\bf{x}}}\) \({\bf{g}}\left( {\bf{x}} \right){\bf{ = }}\frac{{{\bf{x + 1}}}}{{{\bf{x + 2}}}}\)
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