Linear systems are so easy to work with that engineers often construct linear models of
Chapter 5, Problem 1(choose chapter or problem)
Linear systems are so easy to work with that engineers often construct linear models of real (nonlinear) systems to assist in analysis and design. Such models are often surprisingly accurate over a limited range. For example, consider the simple exponential function \(e^x\). The Taylor series representation of this function is
\(e^{x} \approx 1+x+\frac{x^{2}}{2}+\frac{x^{3}}{6}+\cdots\)
(a) Construct a linear model for this function by truncating the Taylor series expansion after the linear term. (b) Evaluate your model function at x = 0.000001, 0.0001, 0.01, 0.1, and 1.0. (c) For which values of x does your model yield a “reasonable” approximation to \(e^x\)? Explain your reasoning.
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