Chapter 1: Q5E (page 1)
Test the series for convergence or divergence.
Given series is
Here, which is greater than zero
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Use the table to evaluate each expression.
(a) \(f\left( {g\left( 1 \right)} \right)\) (b) \(g\left( {f\left( 1 \right)} \right)\) (c) \(f\left( {f\left( 1 \right)} \right)\) (d) \(g\left( {g\left( 1 \right)} \right)\) (e) \(g \circ f\left( 3 \right)\) (f) \(f \circ g\left( 6 \right)\)
\(x\) | 1 | 2 | 3 | 4 | 5 | 6 |
\(f\left( x \right)\) | 3 | 1 | 4 | 2 | 2 | 5 |
\(g\left( x \right)\) | 6 | 3 | 2 | 1 | 2 | 3 |
Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.
If the recommended adult dosage for a drug is\({\bf{D}}\left( {{\bf{in}}\;{\bf{mg}}} \right)\), then to determine the appropriate dosage\({\bf{c}}\)for a child of age\({\bf{a}}\), pharmacists use the equation\({\bf{c = 0}}{\bf{.0417D(a + 1)}}\). Suppose the dosage for an adult is 200 mg.
(a) Find the slope of the graph of\({\bf{c}}\). What does it represent?
(b) What is the dosage for a newborn?
Prove the statement using the\(\varepsilon \), \(\delta \)definition of a limit and illustrate with a diagram like Figure 15.
\(\mathop {\lim }\limits_{x \to 4} \left( {2x - 5} \right) = 3\)
Express the function in the form \(f \circ g\)
\(u\left( t \right) = \frac{{\tan t}}{{1 + \tan t}}\)
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