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Magazine Problem 51
In each pair of equations, one is true and one is false. Choose the correct one. $$ \ln 1=0 \quad \text { or } \quad \ln 0=1 $$
Problem 51
Does the graph of \(a^{x}\) for \(a>1\) have a horizontal asymptote? [Hint: Look at the graph on page 260.]
Problem 52
Does the graph of \(a^{x}\) for \(a<1\) have a horizontal asymptote? [Hint: Look at the graph on page 260.]
Problem 52
In each pair of equations, one is true and one is false. Choose the correct one. $$ \begin{array}{l} \ln (x+y)=\ln x \cdot \ln y \\ \text { or } \ln (x \cdot y)=\ln x+\ln y . \end{array} $$
Problem 52
For each function: a. Find \(f^{\prime}(x)\). b. Evaluate the given expression and approximate it to three decimal places. \(f(x)=e^{x^{2} / 2}\), find and approximate \(f^{\prime}(2)\).
Problem 52
The following problems extend and augment the material presented in the text. a. Show that for a demand function of the form \(D(p)=c / p^{n}\), where \(c\) and \(n\) are positive constants, the elasticity is constant. b. What type of demand function has elasticity equal to 1 for every value of \(p\) ?
Problem 53
In each pair of equations, one is true and one is false. Choose the correct one. $$ \frac{\ln x}{\ln y}=\ln (x-y) \quad \text { or } \quad \ln \frac{x}{y}=\ln x-\ln y $$
Problem 53
For each function: a. Find \(f^{\prime}(x)\). b. Evaluate the given expression and approximate it to three decimal places. \(f(x)=\frac{e^{x}}{x}\), find and approximate \(f^{\prime}(3) .\)
Problem 53
Which will be largest for very large values of \(x\) : \(x^{2}, e^{x}, \quad\) or \(\quad x^{1000} ?\)
Problem 53
The following problems extend and augment the material presented in the text. Show that for a demand function of the form \(D(p)=a e^{-c p}\), where \(a\) and \(c\) are positive constants, the elasticity of demand is \(E(p)=c p\).
