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The functions
{sinmx; cosmx}; m = 0,....∞
form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these with a unique set of coecients. For f(x) = x, we have
To show that the above holds for x = 1, study the di erence between the left- and right-hand sides of the equality as a function of the number of terms included in the sum. Write an octave program to compute and plot the truncated sum approximation (expansion vs x) for n =4 and 16 together with the function x. Make a table showing the error (di erence between two sides) for n =1, 2, 4, 16, 64, 256, 1024. Plot the result of the expansion for 2 values of n together with the original function. Comment on your results. You should submit an octave script or function le I can use to reproduce your results and a separate document (plain text le preferred) for your comments.
The Definition of the Derivative : In the previous section we saw that the calculation of the slope of a tangent line, the instantaneous rate of change of a function, and the ins
Which of the following statements do you think are true about children? Indicate with 'T' for true and for false. Give reasons for your choice. a) Most primary school children a
(x+1/x)^2=3 then value of x^72+x^66+x^54+x^36+x^24+x^6+1 is
Q. a(b - c)x^2 + b(c - a)x + c(a - b) = 0 has equal roots then b = ? Ans: Condition that a quadratic equation ax² + bx + c = 0 has equal roots is: Its discriminant, b² - 4ac = 0 A
3+5
A number x is chosen at random from the numbers -3, -2, -1, 0 1, 2, 3. What is the probability that | x| Ans : x can take 7 values To get |x| Probability (| x |
Find out the Taylor Series for f (x) = e x about x = 0. Solution In fact this is one of the easier Taylor Series that we'll be asked to calculate. To find out the Taylor
(-2x^2y4)(10xy^2)^3
Determine if the line that passes through the points ( -2, -10) and (6, -1) is parallel, perpendicular or neither to the line specified by 7 y - 9 x = 15 . Solution Togive
16 raised to the power x eqaual to x raised to the power 2. find x
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