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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 dierence 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 (dierence 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 vector a → =(2,4) compute 3a → , ½ a → and -2a → . Graph all four vectors on similar axis system. Solution: Now here are the three scalar Multiplication 3a → = (6,
Explain Multiplying/Dividing Negative Fractions? There are 3 steps to multiplying or dividing fractions. 1. If any negative signs are present, place them next to the numerator
1. Sketch the Spiral of Archimedes: r= aθ (a>0) ? 2: Sketch the hyperbolic Spiral: rθ = a (a>0) ? 3: Sketch the equiangular spiral: r=ae θ (a>0) ?
A ?ight from Pittsburgh to Los Angeles took 5 hours and covered 3,060 miles. What was the plane's average speed? Find out the rate at that Susan is traveling through dividing h
what is integration and how is it important
The ratio of the sum of first n terms of two AP's is 7n+1:4n+27. Find the ratio of their 11th terms . Ans: Let a 1 , a 2 ... and d 1 , d 2 be the I terms are Cd's of t
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon
all basic knowledge related to geometry
Need two equal fractions multiply and divide 1/6 3/4 5/15 2/7 20/25 24/36 4/9
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