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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.
Perform the denoted operation. (4/6x 2 )-(1/3x 5 )+(5/2x 3 ) Solution For this problem there are coefficients on each of term in the denominator thus
Q. Illustrate Pythagorean Theorem? Ans. You have definitely seen the Pythagorean Theorem before, so a 2 + b 2 = c 2 should look familiar to you. The Pythagorean Theor
According to a Gallup poll 51% of US women prefer to have a job outside of the home. What is the chance that a survey of 200 women would find that 45% or less of the respondants
How does your answer to this question compare with mine, which follows? i) To begin with, 1 laid the beads out in a row for counting, so that I wouldn't leave any out or count a
Q. Assume a birthday is equally likely to occur in each of the 365 days. In a group of 30 people, what is the probability that no two have birthdays on the same day? Solution:
find the magnitude of the following vectors:5i+7j
A department store faces a decision for a seasonal product for which demand can be high, medium or low. The purchaser can order 1, 2 or 3 lots of this product before the season beg
Kurtosis - It is a concept, which refers to the degree of peakedness of a described frequency distribution. The degree is generally measured along with reference to general di
a) Let n = (abc) 7 . Prove that n ≡ a + b + c (mod 6). b) Use congruences to show that 4|3 2n - 1 for all integers n ≥ 0.
A telephone exchange has two long distance operators.The telephone company find that during the peak load,long distance calls arrive in a poisson fashion at an average rate of 15 p
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