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Lagrange Polynomial Study Questions Example: For given f(x) - sin3x function input-output table is given as below. Find second order Lagrange interpolating polynomial for f(x) using input-output table a. b. Find the f(1,5) value using second order Lagrange interpolating polynomial (Find Lo(x), Lix), and L2(x)) calculate f(x)-sin3x for x:1,5 using your calculator and compare case b result using c. absolute error calculation. (Hint: Use...
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QUESTION 13 Consider a uniform magnetic field B = - Bolz, where Bo is a positive constant and iz points out of the page. A conducting rod sits on the rails of a conducting support of height H containing a resistor R. Some external force is used to move the rod in the x direction according to X(t) = L + at“, where L and a are positive constants. What is the magnitude...
Consider the following function. 5 (7) = rsin (2x), a = 0, n = 4,-0.5 5:50.5 (a) Approximate f by a Taylor polynomial with degreen at the number a. 4 4 2x Talx) 3 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) when x lles in the given interval. (Round the answer to four decimal places.) IRA(X)IS
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r).
1. Consider the polynonial Pl (z) of degree 4...
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Question 24 4 pts Find an equation of the tangent plane to the surface x2 + y2 += 704 at the point (8. - 8, 16). 16(x-3)-96y+8)+ 32-16) = 0 16(x-8)- 48(y+8)+ 32(2-16)=0 16x-8)+ 963 +8)+ 32(-16)0 16x-8)-96(+8)+ 163-16) = 0 16x-8)-96y+8)- 327-16) = 0 Question 25 4 pts Examine the function f(x,y)=x) - 6xy + y + 3 for relative extrema and saddle points. saddle points: (0,0,3),(2,2,-5) relative minimum: (0, 0,...
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f(x) = 10x3-83x2 + 2.295x-0.21 141 = 0 has a root at x-0.29. Use Newton's method with an initial approximation x = 0.28 to attempt to find the root. Explain what happens. 3.
f(x) = 10x3-83x2 + 2.295x-0.21 141 = 0 has a root at x-0.29. Use Newton's method with an initial approximation x = 0.28 to attempt...
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Attempts This lost can only be taken once. Force Once started, this test must be completed in one sitting. Do not leave the test before clicking Save a Completion Your answers are saved automatically. Remaining Time: 1 hour, 29 minutes, 20 seconds. Question Completion Status: Moving to another question will save this response. Question 1 [The Macturin Sereis for the function F(x), M(x) = f(0) + f(O)x+90x+10 a. Find the first four nonzero terms of...
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Assignment5: Problem 11 Previous Problem Problem List Next Problem (1 point) Find the polynomial of degree 9 (centered at zero) that best approximates f(x) = ln(x + 4). Hint: First find a Taylor polynomial for g(x) = ln(x + 4), then use this to find the Taylor polynomial you want. f(x) 1/6 Now use this polynomial to approximate Luca In(x + 4) dx. -1/6 1/6 f(x) dx Assignment5: Problem 12 Previous...
Show that the best possible Lipschitz constant in the second
variable for the function
3(a) Show that the best possible Lipschitz constant in the second variable for the function f(t, x) =-1 1 + x2 is given by K - 9/(8v3) - 3V3/8. Hint: Consider the function fx - (b) Let x, = 1/(1 + x2). Find x"(t) and hence and write down the Taylor method of order 2 for this differential equation. (In the notation of Section 4 of...
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14. 5/14 points | Previaus Answers SCalcETB 11.11.021 Consider the following function. nx) = x sin(x), a = 0, η = 4, -0.9 x 0.9 (a) Approximate fby a Taylor polynomial with degree n at the number a. T4(x) 3! (b Use Taylor's Inequality to estimate the accuracy of the approximation IR4(x) 0.0005 when x lies in the given interval. Round M up...