This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the questions: QUESTION ONE (a) Define/State the following: (i) Hyperbolic functions Hyperbolic functions are a set of functions mathematically analogous to the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. They are typically defined in terms of the exponential function, for example, x = e^x - e^-x2 and x = e^x + e^-x2. (ii) Comparison Test The Comparison Test is a method used to determine the convergence or divergence of an infinite series or an improper integral by comparing it with another series or integral whose convergence or divergence is already known. For example, if $0 a_