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1. In using Newton's method to find a root of an equation f(x) = 0, with initial guess x0 = 3, we compute 1(x0) = 1, and find that x1 = 5. What is fl(x0)?
2. Let a be a given number and suppose that 0 < e < 1 is also a given number, Show that the equation a = x - e sin x has a unique solution and it can be found by fixed point iteration of an appropriate function with any starting value.
3. The following formula is used to compute a function f:f (x) = N/ - ¦/r-2Suggest a more accurate way to compute the same function.
4. The reciprocal of a number R can be computed by the following iteration (no divisions!):Xn+1 = ZIP - XnR).This is Newton's method applied to find the zero of a certain function f. What is f?2k-1-1 = Xk 2Xle + 2n"le - uj4: z2= -Xk + 42k - 2a) What is p(x)? What are its roots?1)) One of the iterations will converge to either of the two roots of p(x) if the initial guess is sufficiently close. Each of the others will converge to one root, but can't possibly converge to the other unless the initial guess is exactly equal to the root. Which is which? Give a justification for your answer.
Find the probability that a randomly selected degree is not in Business & is not in Engineering?
Find all critical numbers (x coordinates). Where is the function y = f(x) increasing? Where ia the function y = f(x) concave down? Find the x-coordinate of the inflection point.
who were over age 18 was approximately 2.28 x ?10?^8 people if the national debt were evently didvided among every person over age 18 in the country how much debt would be assigned to each individual? Round to three significant digits.
Which of the properties: reflexive, antisymmetric and transitive are true for the given relation? Begin your discussion by defining each term in general first and then show how the definition relates to this specific example.
Where G is the geometry matrix [p0 p1 p2 p3] and u (t) is the column vector (1, t, t2 , t3). In a uniform B-spline, each segment uses the same basis matrix, but the geometry matrix changes. Construct the basis matrix MS for x(t).
If 1600 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Suppose you wish to build a spa on a wood deck. The deck is to be built 4 ft above level ground. It is to be 50 ft by 30 ft and is to contain a spa that is circular with a 14-ft diameter. The spa is 4 ft deep.
certain drug is made out of two compounds only: A and compound B. To make this drug 6 parts of compound A are used for every 5 parts of compound B. If a chemist wants to make 957 milliliters of this drug, how many milliliters of compound B are nee..
you decide to invest 15000 into a bank account that that is compounding its interest monthly. assuming the bank is
Find the probability that a male resident who was newly diagnosed with AIDS in 1998 contracted it via homosexual contact. Find the probability that a female resident who was newly diagnosed with AIDS in 1998 contracted it via intravenous drug use.
Find the vector equation of the line through the origin and perpendicular to the line given by r(t) = . (Recall: Two lines are perpendicular if they intersect at a right angle.)
Identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters
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