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If f(x) = f(-x) for all x, then the graph of f(x) is symmetric with respect to the y-axis, and the function f(x) is called an even function. If f(x) = -f(-x) for all x, the graph of f(x) is anti-symmetric with respect to the origin, and we call such a function an odd function a. Show that any function can be written as the sum of an odd function plus an even function. List as many even and odd functions as you can. b. State what conditions must be true for a polynomial to be even, or to be odd. \c. Show that the product of two even functions is even; the product of two odd functions is even; and the product of an odd and even function is odd. d. Replace in c above the word product by either quotient or power and deduce the parity of the resulting function. e. Deduce from the above results that the sign/parity of a function follows algebraic rules.
f. Find the even and odd parts of the following functions: (i) f(x) = x7 + 3x4 + 6x + 2 (ii) f(x) = (sin(x) + 3) sinh2(x) exp(-x2)
write a create table statement that recreastes the table, this time with a unique constraint that prevents an individual from being a memeber in the same group twice.
Using a PLD, develop an I/O port decoder that generates the following high-bank I/O strobes: 300DH, 300BH, 00B6H, and 00EEH.
Has its creation increased or decreased the need for organizations to maintain secure operation of their systems? Why?
Consider coordinates xµ = (x 0 , x 1,x 2 , x 3) and the associated light-cone coordinates (x+ , x -,x 2 , x 3 ). Write the following Lorentz transformations in terms of the light-cone coordinates:
Explain why replacing the extracellular with choline has little effect on the resting potential of an axon. Calculate the new resting potential with 90% of the extracellular removed. Why is the same not true if is replaced? (Assume the conductance..
A brief description (a paragraph of 100-200 words) providing the project background/context. e.g. is it based on a business need? a technical need? does it arise from the interests of a particular person/company?
Write a program that generates a random integer in the (inclusive) range [0-9] (i.e. the set {0,1,2,3,4,5,6,7,8,9}) and ask the user to guess what the number is.
Boardman plans to hire Smith Systems Consulting to help them analyze their options and to create the implementation plan.
Let P be a problem. For any instance x ∈ P, the solution is some real number f(x). Let A be a randomized algorithm for P, such that it gives a solution A(x) that lies in [1/2f(x), 2f(x)] with probability 2/3.
What happens to mycp if one or more of the files to be copied doesn't exist? Can you make any suggestions to better handle the situation?. Write a program called mymv that does with the mv command what mycp does with the cp command. How many changes ..
Calculate the total price based on several key parts required to build a state-of-the-art gaming computer. The user will have the option of selecting different parts. For example, Windows 7, Windows 8 or Mac OS/X for Operating systems, 4 GB, 8 GB or ..
What is TPM? Trusted Computing Group Note: Include a discussion of TPM as a specification vs. TPM as an implemented product/system. Also include discussion of current specification,
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