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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 x-coodinate of the local maximum of f(x) = x3 - 2.3x2 - 2.8x. Find the x-coodinate of the local maximum of f(x) = x3 - 2.1x2 -1.7x.
Let R be the shaded region in the first quadrant enclosed by the graphs of y=e^(-x^2), y= 1-cos x, y-axis.
MATH 54 QUIZ 3. Let T(x, y) = (3x + 2y, x - y). Show that T is a linear transformation. Is T one-to-one? Is T onto
A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before filming begins. Two teams are available, one that requires 700 hours and one that requires 500hours. If the teams work tog..
Find a vector valued function that represents the intersection of z2 + x2 = 9 and z + y = 10. Draw the curve. Use trigonometry to parameterize efficiently.
Structure 1 (5 m x 5 m) has a bearing pressure of 36.5 kN/m2, and structure 2 (10 m x 10 m) has a bearing pressure of 80 kN/m2. Determine the MAGNITUDES of the effective vertical (z) and the shear stress in the x-z plane at point A
Find the equation of the line and you can write your answer in the following form: p = mx + b. Normally in this class, you would probably use the "y = mx + b" format. You are basically substituting the variable "y" with "p"
a college bookstore has been selling one particular tee shirt for a year now. during the fall term 100 were sold at a
An airplane is flying in the direction 148 degrees with an airspeed of 860 km/h. Because of the wind, its groundspeed and direction are, respectively, 800 km/h and 140 degrees. Find the direction and speed of the wind.
you are considering starting a walk-in clinic. your financial projections for the first year of operations are as
Plot each z-value along the horizontal axis, and each corresponding x-value along the vertical axis. These points should be collinear. What is the slope and intercept of the line through these points? How do they relate to the distribution of X
An object with mass m1=1 kg, moving with velocity v1=5.00 m/s, has a perfectly inelastic collision with other object, having mass m2=3 kg in rest (v2=0 m/s). After the collision, two objects are stuck together and move with velocity v3. Calculate val..
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