Chapter 3: Q34E (page 189)
To find the derivative of the function \(y = sinh(coshx)\).
The derivative of the function \(y = \sinh (\cosh x)\) is \(\sinh x\cosh (\cosh x)\).
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(A) to determine the function\(f(x) = \frac{1}{{x - 1}},\;x > 1\)is one-to-one.\({f^{ - 1}}(x) = \frac{1}{x} + 1\)in
(B) To determine the value of\({\left( {{f^{ - 1}}} \right)^\prime }(2)\), where\(f(x) = \frac{1}{{x - 1}}\).
(C) To determine the inverse of the function\(f(x) = 9 - {x^2}\)and state its domain and range.
(D) To determine whether the value of\({\left( {{f^{ - 1}}} \right)^\prime }(2)\)is\(\frac{1}{4}\)using the inverse function.
(E) To sketch: The graph of\(f(x) = \frac{1}{{x - 1}}\)and\({f^{ - 1}}(x) = \frac{1}{x} + 1\)in the same coordinate.
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.
7.\(\mathop {lim}\limits_{\theta \to \frac{\pi }{2}} \frac{{1 - sin\theta }}{{1 + cos2\theta }}\).
Determine the inverse of a function \(m = f(v) = \frac{{{m_0}}}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }}\) and interpret the meaning.
To determine the value of \(\mathop {\lim }\limits_{u \to \infty } \frac{{\left( {\frac{{{\varepsilon ^u}}}{{10}}} \right)}}{{{u^3}}}\).
(a) To determine the graph of functions \(cschx, sech x\), and \(\coth x\) by using graph of the functions \(\sinh x,\cosh x\), and \(\tanh x\).
(b) To check the graphs sketched in part (a) and using graphing device to draw the graphs.
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