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(a) Calculate the inverse Fourier transform h(x) of h(k), where h(k)= 0 for b for -b for 0 for k<-a, a a, and a, b are some real positive constants. Express your final answer in terms of sines and/or cosines (as opposed to exponentials).

(a) Calculate the inverse Fourier transform h(x) of h(k), where h(k)= 0 for b for -b for 0 for k<-a, a a, and a, b are some real positive constants. Express your final answer in terms of sines and/or cosines (as opposed to exponentials).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.5: Derivatives Of Logarithmic Functions
Problem 56E: This exercise shows another way to derive the formula for the derivative of the natural logarithm...
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please help me out. details and explanations are very much appreciated

3. (a) Calculate the inverse Fourier transform h(x) of h(k), where (b) (c) h(k)= 0 for b for -b for 0 for and a, b are some real positive constants. Express your final answer in terms of sines and/or cosines (as opposed to exponentials). where With the help of Table 1, determine the inverse Laplace transform f(t) of is a Heaviside function. k<-a, a <k<0, 0<k<a, k > a, F(s) = Using the method of Laplace transform, solve the following initial value problem: e-7(+2) (s+ 2)² - 25 ÿ + 5y + 6y = (sin t)[H(t) - H(t-2n)], y(0) = 0, y (0) = 0, H(t-a)= for t > a, 10 fort <a,
Transcribed Image Text:3. (a) Calculate the inverse Fourier transform h(x) of h(k), where (b) (c) h(k)= 0 for b for -b for 0 for and a, b are some real positive constants. Express your final answer in terms of sines and/or cosines (as opposed to exponentials). where With the help of Table 1, determine the inverse Laplace transform f(t) of is a Heaviside function. k<-a, a <k<0, 0<k<a, k > a, F(s) = Using the method of Laplace transform, solve the following initial value problem: e-7(+2) (s+ 2)² - 25 ÿ + 5y + 6y = (sin t)[H(t) - H(t-2n)], y(0) = 0, y (0) = 0, H(t-a)= for t > a, 10 fort <a,
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