Chapter 3: Q3E (page 161)
Determine whether the function given by a table of values is one-to-one.
The resultant answer is not a one-to-one function.
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To determine the value of \(\mathop {\lim }\limits_{x \to {2^ + }} \left( {{e^{\frac{3}{{2 - x}}}}} \right)\).
(a)The function\(f(x) = \sqrt {x - 2} \)is one-to-one.
(b) The value of\({\left( {{f^{ - 1}}} \right)^\prime }(2)\), where\(f(x) = \sqrt {x - 2} \)
(c) The inverse of the function\({\left( {{f^{ - 1}}} \right)^\prime }(2)\)and state its domain and range.
(d) Whether the value of\({\left( {{f^{ - 1}}} \right)^\prime }(2)\)is 4 using the inverse function.
(e) Sketch the graph of\(f(x) = {x^3}\)and\({f^{ - 1}}(x) = {x^2} + 2\)in the same coordinate.
Sketch the graphs of the function \(y = {0.9^x},\;y = {0.6^x},\;y = {0.3^x}\)and \(y = {0.1^x}\) on the same axes and interpret how these graphs are related.
(a) To show any function of the form \(y = Asinhmx + Bcoshmx\) satisfies the differential equation\({y^{\prime \prime }} = {m^2}y\).
(b) To determine the function \(y = y(x)\).
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.
11.\(\mathop {lim}\limits_{t \to 1} \frac{{{t^8} - 1}}{{{t^5} - 1}}\).
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