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1. NCM problem 1.8. Be sure ansuer the questions asked in the problem particular, you figure out what the matrix elements that are being generated are (lock chapter come answerl. 2. NCM. problem 1.34. Don't just explain what ench line code the and what the values should be 3. NCM. probless 1.35 4. NCM. problem Make <]) thoroughly This best by setting dome and x(2) Make sure yom compate the accurate the formula book 5 NCM. problem 1.45 Note the (a) blance 6. According the Richter M given formula where Ei the energy 1044 Joules the energy of depends the function plot and make ased to create 7. The history history mathematics that There many amazing formulas for computing which was used by James Gregory 1671 compute many digits. Another infinite series involving Basel serins go- (2) which Leonhard Euler proved 1735 (a) Write Matlas function for approximating using the Basel series. Your fuaction should aumber the Basel series and ostpat an approximation to z. Using this fuaction othe following i. Compute an approximation t using 10.10P, 10³. 104. 10². and 10 term in the serim report table ii. Compute asing the built-in comstant for from MAT- ad report the results same table. iii. Plot the function the aumber tesms used i the sum Use the and axes of your plot obtain the erron plot a your assignment (b) You should motice from part (a) that the series does not converge very This one ofthe Euler the series 2/6 they zouldn't surm emough terms make guess what the answer might be Euler grentness, notiond thet the Basel series could follows (3) where log here the natural logarithm This rees much more and Euler (whe was closest thing this world may have seem humm the toget what might converge to be later he resalt) Write MATLAR function for Euler's the Basel series Asit part (a). your function the total number the Basel series Using this function do the following Compute approximation using and 2 terms the series report the results in table ii. the built-in constant for from MAT- report the results the same table. Plot relative error the approximation function of the number terms the sum Use a the and y Eyour plot obtain the error curve Include this plota your assignment (c) None a for however. compare the following one ered by John Machin in 1706 (4) This formula particularly nace cal involves rational numbers and the term zeto very rapadly. this formula Machin was able to 100 Write Mailab function formula Asi part and series and ompet an approximation tox. part 2(b)(i) (iii) using your function Note that there now mach better than the ones listed abore 8. Let r and y be column polygion (given order that polygion without repeating vertion, first ones). The polygion can computed using formula where assurmed that the vertices i.e. Fa+l 91 (a) Write a MATLAB function that takes input vectors and containing the vertions polygon Computes the result. Try the use loops by being function sum and vec- toruzation Producs displayed Labels polygion the title (b) Test your pentagon, and regular resuats that E one that has 9 (Area (g) states think the state border Use these estimate and thast total number 1356 polygon representing Idaho problem obtain the region Idaho, of for distances betareer earth Idaho, use some geometrical tricke to convert points values miles Compare you answer "official' Idaho Make sure yom explair hom and what between your estimate and the the programas pi, for, while, sun, if, xlabel ylabel title these >>help MATLAB command

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1.
Matrix X starts as the identity matrix while matrix A is the operation of adding numbers according to the Fibonacci series; that is matrix X updates with the latest Fibonacci numbers. Every time enter is pressed we get the next number sequence in the Fibonacci series. n=0@X(2,2), n=1@X(2,1), n=2@X(1,1)=[X(2,2)+X(2,1)].
The process has to be repeated 1475 until X overflows, at the 1476th time the sum of numbers will be greater than realmax (=inf).

2.
e (expected)   = 0 0 0 0 0 0 0 0 0 0
e (calculated) =   1.0e-15 *
         0         0   -0.0555         0         0         -0.1110   -0.1110         0         0         0

t is a scalar. n is an array (size 10). Thus n determines the size of e, which is a size 10 array.
Each of n array values is similarly calculated, and should be zero (since: n/10 – n*0.1=0). This however is seen to not be the case.
MATLAB expresses divisions (1/10, etc.) as a binary approximation using an infinite series, up to a 52 bit term precision. In the above the decimal number 0.1 is developed into a series with a representation error, known as a round-off error. That is why, for example, the result of 3/10 differs slightly from 3*(1/10) and we are left with a non-zero result....
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