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1. Show that the points 1, ein/2, -1, e137/2 are points equally spaced on the unit...
A 1. Let 2n (equally spaced) points ways to join these points in pairs intersect, equals the nth Catalan number C on a...
A 1. Let 2n (equally spaced) points ways to join these points in pairs intersect, equals the nth Catalan number C on a circle be chosen. Show that the number of so that the resulting n line segments do not
A 1. Let 2n (equally spaced) points ways to join these points in pairs intersect, equals the nth Catalan number C on a circle be chosen. Show that the number of so that the resulting n line segments do not
4. (25 pts) Given a function f with three continious derivatives, and three equally spaced points...
Parts b and c please
4. (25 pts) Given a function f with three continious derivatives, and three equally spaced points zi z, = zi+h, エ3年エ1 + 21, we would like to approxinate f'(z), Let p(z) be the quadratic polynomial interpolating ()) (a) Write p in the Lagrange form. (b) Show the forward difference formula (c) Prove that this expression is a second order approximation off,(r), that is, show that where C depends on the third derivative of f.
4....
Assume that 2(r+b) points, with rbe N, are drawn on a circle, equally spaced (thus, the...
Assume that 2(r+b) points, with rbe N, are drawn on a circle, equally spaced (thus, the rays from the center of the circle to any two adjacent points are at an angle of (r + b) radians). Assume also that 2r of the points are colored red and that the other 2b are colored blue. (You do not get to choose which points get which color.) Must there be at least one rotation of the circle through its center that...
Ten points P1, P2,...,P10 are equally spaced around a circle. They are connected in separate pairs...
Ten points P1, P2,...,P10 are equally spaced around a circle. They are connected in separate pairs by 5 line segments. How many ways can such line segments be drawn so that only one pair of line segments intersect?
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr...
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr. Using the rigorous error n should be in order that li-Tal 3x 10-0
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error...
(1) Let qn(x)-IT-1 (z-zi) where the xi, į = 1, , n are equally spaced: zi+1-z-h...
(1) Let qn(x)-IT-1 (z-zi) where the xi, į = 1, , n are equally spaced: zi+1-z-h for some h > 0. Let a (a) Show 21 and b zn. zela阎 (b) Show
5. (a) The natural spline S(a) passing through the n+ points is a collection of n cubic functions S,(x) defined in the n intervals x, Sxx Suppose that all the points are equally spaced, with unifo...
5. (a) The natural spline S(a) passing through the n+ points is a collection of n cubic functions S,(x) defined in the n intervals x, Sxx Suppose that all the points are equally spaced, with uniform point spacing h=5m-x, for jso,1,..,,n. Ifthe symbols M,, 0, represent the second derivatives of the spline at cach of the mesh points, show that in each intervl-.R-1 For the natural cubic spline (for which M, O and M-=0 ), show that the moments M...
Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state...
Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state conductive heat transfer through a metal rod and convection to the surrounding air, which are described by the following ordinary differential equation: T" – TQ2 = -a?T. T(x = 0) = 0 T(x = L) = 2 T is the temperature distribution in a rod, a = hP/kA, h is the heat transfer coefficient, P, A and L are the perimeter, the cross section...
show all working please 10 Given z = 2 – j2 is a root of 2z'...
show all working please
10 Given z = 2 – j2 is a root of 2z' - 9z2 + 202 - 8 = 0 find the remaining roots of the equation. Find the real and imaginary parts of z when 1 2 1 2 2 + j3 3 - 2 .. Find z = Z4 + z2z3/(z2+z3) when 2, = 2 +j3, z2 = 3 + j4 and 23 = -5+j12. Find the values of the real numbers x and...
1/2 points Three balls, with charges of +4q, -2q, and -q, are equally spaced along a...
1/2 points Three balls, with charges of +4q, -2q, and -q, are equally spaced along a line. The spacing between different ways, as shown in the figure. In each case, the balls are in an isolated region of space very far from anything eise. 2 (a) Rank the three cases, from largest to smallest, based on the magnitude of the net force experienced by the ball with the +4q charge. (Use only "or"symbols. Do not include any parentheses around the...
A 1. Let 2n (equally spaced) points ways to join these points in pairs intersect, equals the nth Catalan number C on a circle be chosen. Show that the number of so that the resulting n line segments do not
A 1. Let 2n (equally spaced) points ways to join these points in pairs intersect, equals the nth Catalan number C on a circle be chosen. Show that the number of so that the resulting n line segments do not
Parts b and c please
4. (25 pts) Given a function f with three continious derivatives, and three equally spaced points zi z, = zi+h, エ3年エ1 + 21, we would like to approxinate f'(z), Let p(z) be the quadratic polynomial interpolating ()) (a) Write p in the Lagrange form. (b) Show the forward difference formula (c) Prove that this expression is a second order approximation off,(r), that is, show that where C depends on the third derivative of f.
4....
Assume that 2(r+b) points, with rbe N, are drawn on a circle, equally spaced (thus, the rays from the center of the circle to any two adjacent points are at an angle of (r + b) radians). Assume also that 2r of the points are colored red and that the other 2b are colored blue. (You do not get to choose which points get which color.) Must there be at least one rotation of the circle through its center that...
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error bound for 1-Tr. Using the rigorous error n should be in order that li-Tal 3x 10-0
(35) Problem 5. 2) e Consider using the composite trapezoidal rule T7, with n equally spaced u rule Tn with n equally spaced subintervals to estimate I-In zdz Give a rigorous error...
(1) Let qn(x)-IT-1 (z-zi) where the xi, į = 1, , n are equally spaced: zi+1-z-h for some h > 0. Let a (a) Show 21 and b zn. zela阎 (b) Show
5. (a) The natural spline S(a) passing through the n+ points is a collection of n cubic functions S,(x) defined in the n intervals x, Sxx Suppose that all the points are equally spaced, with uniform point spacing h=5m-x, for jso,1,..,,n. Ifthe symbols M,, 0, represent the second derivatives of the spline at cach of the mesh points, show that in each intervl-.R-1 For the natural cubic spline (for which M, O and M-=0 ), show that the moments M...
Apply the finite difference method (with equally spaced 4 points grid) for solving a steady state conductive heat transfer through a metal rod and convection to the surrounding air, which are described by the following ordinary differential equation: T" – TQ2 = -a?T. T(x = 0) = 0 T(x = L) = 2 T is the temperature distribution in a rod, a = hP/kA, h is the heat transfer coefficient, P, A and L are the perimeter, the cross section...
show all working please
10 Given z = 2 – j2 is a root of 2z' - 9z2 + 202 - 8 = 0 find the remaining roots of the equation. Find the real and imaginary parts of z when 1 2 1 2 2 + j3 3 - 2 .. Find z = Z4 + z2z3/(z2+z3) when 2, = 2 +j3, z2 = 3 + j4 and 23 = -5+j12. Find the values of the real numbers x and...
1/2 points Three balls, with charges of +4q, -2q, and -q, are equally spaced along a line. The spacing between different ways, as shown in the figure. In each case, the balls are in an isolated region of space very far from anything eise. 2 (a) Rank the three cases, from largest to smallest, based on the magnitude of the net force experienced by the ball with the +4q charge. (Use only "or"symbols. Do not include any parentheses around the...
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