It is solved with the following function:
f(x) = A sin(n*π*x/L) Maximum
If the function is defined between zero and L, find where it is at
a maximum. In terms of probability, what is this telling you
physically?
Probability
For n = 4, write down (but do not solve) the integral you would
need to evaluate to see if the object is between 0 and L/3. Please
include a sketch.
1)
for
Then the maximum occurs for
This means the object is most likely to be found at the middle
2) Sketch to explain the situation:
The set-up of the integral is:
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It is solved with the following function: f(x) = A sin(n*π*x/L) Maximum If the function is...
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that the function can be extended and modelled as a Fourier cosine-series: (a) Sketch this extended function in the interval that satisfies: x <4 (b) State the minimum period of this extended function. (C) The general Fourier series is defined as follows: [1 marks] [1 marks] F(x) = 4 + ] Ancos ("E") + ] B, sin("E") [1 marks] State the value of L. (d)...
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1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of period 2L by using an odd half-range expansion 1) Sketch the extended function over the interval -3L<XS3L. 2) Calculate the coefficients for the Fourier Series representation of the extended function. 3) Write the first 5 non-zero terms of the Fourier Series. (10 marks)
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1. (a) Evaluate the Fourier coefficients a, an, ba for the function defined as f)-2 cos() for-π/2 s sn2 and zero else over the period of 2T, do NOT use MATLAB or a calculator for integrations. All the steps should be shown. Write a few terms of the Fourier series expansion Plot 2 or 3 cycles of the Fourier series using MATLAB and verify whether the plot matches the given waveform Find Co and Cn and plot the amplitude spectrum...
4. Let X have the following PDF: sin(x) , 0 < x < π , otherwise Ix(x) = 0 Find the CDF of X Using the Probability Integral Transformation Theorem, describe the process of generating values from the density of X Using R, generate 1,000 values using your process in part b. Produce a histogram of these generated values, and overlay the density curve of X over top. (Hint: in R, the function acos calculates the inverse cosine function.) Using...
3. On the open interval (0, π/2), a function f with f'(x) = sin(x^2 ) must be (choose one, and explain your answer): (a) increasing and concave up (b) decreasing and concave up (c) increasing and concave down (d) decreasing and concave up (e) None of the above
someone please help me solve this question 5(a,b,c). thank
you!!!
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