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Question:
Consider the equation
cos (Πx) - x3 = 0.
(a) Use MATLAB to plot a graph on any interval you consider appropriate that shows all roots of this equation. Provide argunimits that there are rm other roots.
(b) Give a reason why the iterative scheme
xn+1 = [cos(Πxn)1/3,
is not suitable for determining a sequence that converges to the largest positive root starting from xo = 0.5.
(c) Find a suitable rearrangement such that the sequence starting with xo = 0.5 converges to the largest positve root. Show that your rearrangement satisfies the criteria of Theorem.
(d) Determine an approximation to the largest positive root up to 10-6 accuracy.
(e) Explain how you can estimate the number of iterations needed.
(f) Argue why the estimated number of iterations needed does or does tot differ from the actual number of iterations needed in part (d).
Design op amp integrators and differentiators using negative feedback but with induc¬tors instead of capacitors. (In most situations, capacitors are less expensive than induc¬tors, so the previous designs are preferred.)
Use the mathematical and graphical analyses to determine the equation of the above function if the parabola cross the line y=2x at two points with the x-coordinates 0 and 10. and determine the domain and range of the variables
Make a 95 percent confidence interval on the variable age.
The altitude h (in meters) of a jet as a function of the horizontal distance x (in kilometers) it has traveled is given by:
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the aera of a rectangular wall in a classroom is 126 square feet. it lenght is 3 feet shorter than three times its width. find the length of the wall of the classroom.
The dimensions of a closed rectangular box are measured as 90 cm, 65 cm, and 34 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.
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let a b and c be three noncollinear points and let p be a point in the interior of angle bac. then p lies on the angle
The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 80 mph can stop i n360 ft, how many feet will it take the same car to stop when it is traveling 70 mph?
Differentiate the function f(x)
A rectangle is 6 kilometers less than twice its length if its area is 216 square kilometers find the dimensions of the rectangle.
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