Chapter 1: Q44E (page 10)
Find an expression for the function whose graph is the given curve. The line segment joining the points (-5, 10) and (7,-10).
The expression for the function is\({\bf{y = - }}\frac{{\bf{5}}}{{\bf{3}}}{\bf{x - }}\frac{{{\bf{16}}}}{{\bf{3}}}\).
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Evaluate the difference quotient for the given function. Simplify your answer.
\(f\left( x \right) = 4 + 3x - {x^2}\), \(\frac{{f\left( {3 + h} \right) - f\left( 3 \right)}}{h}\)
Find
(a) \({\bf{f + g}}\)
(b) \({\bf{f}} - {\bf{g}}\)
(c) \({\bf{fg}}\)
(d) \({\bf{f}}/{\bf{g}}\)
and state their domains.
37. \({\bf{f}}\left( x \right) = {x^3} + 2{x^2}\) \(g\left( x \right) = 3{x^2} - 1\)
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 |
Prove the statement using the \(\varepsilon ,\)\(\delta \)definition of a limit and illustrate with a diagram like a Figure 15.
\(\mathop {\lim }\limits_{x \to - 3} \left( {1 - 4x} \right) = 13\)
Determine whether\({\bf{f}}\)is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually.
64.\({\bf{f}}\left( {\bf{x}} \right){\bf{ = 1 + 3}}{{\bf{x}}^{\bf{3}}}{\bf{ - }}{{\bf{x}}^{\bf{5}}}\)
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