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Question: tmobile lte 5496 0 1529 homepagesmathuicedu proximation 14...

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T-Mobile LTE ขึ 5496 @.0. + 15:29 homepages.math.uic.edu proximation 1.4 for Assignments 1. Explain the outcome of 3-45. In particular, what is the order of execution of the two exponentiation operations? 2. Write s -1 as a product of prime numbers. 3. The greatest common divisor of two integer numbers a and can be written as a linear combination (with integer coeffi- cients & and) of a and b: godia, bkah In Sage this is achieved with the command xged. Look in the help page of this command to compute the coefficients of the linear combination of the greatest common divisor of 12214 and 2012. Give the command you type in to find these coefficients and also give the command(s) to verify the result. 4, what is the difference in Sage between 1/3+1乃+1 and 103+103+103 Explain. 5. Consecutive rational approximations for π are 3, 22/7 333/106, 355/113, In this sequence, what is the next more accurate rational approximation for? How many deci- mal places are correct in this next rational approximation? 6. Explain the difference between 10+0 and. How can you make Sage return the same correct value of these two sums? 7. The golden ratio is defined asGive all Sage 0) to compute a rational approximation for accurate with three decimal places; (l) to show that the accuracy of this approximation is indeed three decimal places; (ili) to compute a sequence of the first ten consecutive ratio- nal approximations, where the k-th number of the sequence is accurate with k decimal places. 8. Consider 1.2599. Find the algebraic number that is clos- est to r. 9. Consider 3. Compute the first ten terms in the continued fraction expansion. Write the last element in the correspond- ing list of convergents. Compare the floating-point approximation of this rational ap- proximation for 3 with the floating-point approximation for . How many decimal places in the rational approximation are correct? Give the floating-point approximation of the rational approxi- mation for 3. Write only those decimals that are correct.
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