Chapter 3: Q17E (page 150)
Find the exponential function which is of the form \(f(x) = C{b^x}\) for the given graph.
The equation of the graph is \(f(x) = 3{(2)^x}\).
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To determine the point of the curve\(y = coshx\)when the curve has slope \(1\).
1–38 ■ Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.
10.\(\mathop {lim}\limits_{x \to \infty } \frac{{ln\sqrt x }}{{{x^2}}}\).
To determine the value of \(\mathop {\lim }\limits_{u \to \infty } \frac{{\left( {\frac{{{\varepsilon ^u}}}{{10}}} \right)}}{{{u^3}}}\).
1–38 ■ Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.
2. \(\mathop {lim}\limits_{x \to 2} \frac{{{x^2} + x - 6}}{{x - 2}}\).
Show that if \(a \ne 0\) and \(b \ne 0\), then there exists \(\alpha \) and \(\beta \) such that \(a{e^x} + b{e^{ - x}}\) is equal to either \(\alpha sinh(x + \beta )\) or \(\alpha cosh(x + \beta )\). In other words, almost every function of the form \(f(x) = a{e^x} + b{e^{ - x}}\) is a shifted and stretched hyperbolic sine or cosine function.
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