In each of the following problems you are given a function on the interval
Sketch several periods of the corresponding periodic function of period
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- 4. Sketch several periods of the following function: f (x) 0,- piarrow_forwardProblem 4 Is the given function even or odd or neither even nor odd? Find its Fourier series. Show details of your work. 2arrow_forwardThis question is about: In each of Problems 11 through 16: (a) Sketch the graph of the given function for three periods. (b) Find the Fourier series for the given function. The equation is in the first picture. My question is why the textbook wrote the answer like the second picture show. Why, for the cos part, why you have coefficient 2/(2n-1)^2? Would you please give me a clear explanation? I am bewildered. I was thinking we need to get an and bn then plug into the original equation, then will be fine.arrow_forward3. Suppose a sinusoidal function was created to model a yearly lynx population, due to a cyclical pattern of increasing and decreasing throughout each year. This function can take the form of y = a cos[ b (x - c)] + d Explain what the value of each parameter (a, b, c and d) would represent in the real-life context of analyzing lynx populations. If you were analyzing the function, consider what each parameter could tell you about the population or the time of research.arrow_forwardConsider the following. -2 SxS -1, (x) -7x, -1arrow_forwardProblem 5 Sketch the graph and find the Fourier series of the 2n-periodic extention of the function f(x) = e", a E (-7, "). Find the sum of the Fourier series you obtained at points r and 27.arrow_forwardPlease provide the solution and correct answer and box the final answer/s. Express answer (nonterminating or repeating decimal) using 10 digits as seen in your scientific calculator.arrow_forward3. The water at a local beach has an average depth of 1 meter at low tide. The average depth of the water at high tide is 8 m. If one cycle takes 12 hours: (a) Determine the equation of this periodic function using cosine as the base function where o time is the beginning of high tide. (b) What is the depth of the water at 2 am? (c) Many people dive into the beach from the nearby dock. If the water must be at least 3 m deep to dive safely, between what daylight hours should people dive? Time (h) Height (m)arrow_forwardQ.3. Find the fourier expansion for the function whose definitionarrow_forwardarrow_back_iosarrow_forward_iosRecommended textbooks for you
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