Find the Maclaurin Series of the following functions. sin(x')
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A: Given: Sin x, Cos x and exand To prove that: d/dx(sin x)=cos xd/dx (cos x) = − sin x and d/dx (ex)…
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A: The Maclaurin series is given as f(x) = f(0)+xf'(0)+x22!f''(0)+x33!f'''(0)+x44!fiv(0)+x55!fv(0)+...…
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Q: & Expand the following functions into Laurent series in a neighborhood of point =0: sin': %3D %3D
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- If f(t)= t2-2t where 0< t< find the following 1) The cosine series. 2) The sine series.M9Leslie matrix the Leslie matrix, which is used to model population growth. Consider the following example that looks at the population of an isolated colony of female beetles. Assume that the beetles live at most four years, we can divide them into four age groups (0-1, 1-2, 2-3, 3-4). Suppose that the initial population of 100 beetles (at year 1) records 30, 35, 25, 10 individuals for each corresponding group. Suppose that the birthrates for each of the groups are 0, 4, 2, and 1 per year. That is, beetles do not produce any young female in the first year of life, and they produce one young female in the fourth year. Suppose that the survival rate for each class is given by 0.7, 0.5, 0.2,0. A way to express the population at year 2 for each age group is the following: 4 1 30 0.7 35 0.5 25 0.2 0 10, Explain in words why the population of beetles at year 2 should be given by the above matrix multiplication.
- #18 (A)Sketch the odd and even extension for given function below. Then find the Fourier sine series for the given interval. L if 0For 1 and 2?Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,