4. The "bi-secant method" is a combination of the secant method and the bisection method.As in the case of the secant method, it uses two points (a, f(a)), (b, f(b)) to find a secant linethat goes through those points and computes a point c where the secant intersects the r axis.As in the case of the bisection method, we require that f(a)f(b) < 0, and assuming thata Question continued(c) Notice that if there is a sign change in the function from a to c then the solution is in [a, c]otherwise, the solution is in [c, b]Use the description above, and your formula for c to write the bi-secant algorithmsuch that that given f(r), a, b, e, N returns an approximation to the solution of f(r) witherror tolerance e, or an error, if the number of iterations exceeds N

Let the curve be y=f(x) , Given, initial and final points of curve is a, f(a) and b,f(b)…

Answered: 4. The "bi-secant method" is a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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If p(x, y) = (y+2, 2-x) and u(x, y) = (x, -y), find the formula p∘p∘u and us it to determine its fixed points and stable lines.
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Q3.If f(x,y)=sin²(x-3y)+sin(xy find: Q4. Use Lagrange multipliers to find the shortest distance between the origin and the plane contains the points (1,2,-1), (3,5,9), and (-1,2,-5). af and and aj
Find the equation of the line which passes through the point (1, 2, –3) and is perpendicular to the plane 2x + y + 3z = 4. Express your answer in the form r(t) = f(t) i+ g(t) j+ h(t) k, where f(t), g(t) and h(t) are functions you should specify.
G(-3, 2) is translated using the rule (x,y) → (х-2, у-5). Your answer F(-2, 4) is rotated 90° clockwise about point (0,0). Your answer A(3, -8) is reflected in the x-axis. Your answer K(-5, 2) is dilated with a scale factor of 0.5 centered at the origin. Your answer L(4, 3) is dilated with a scale factor of 3 centered at the origin. Your answer B(-2, 7) is reflected in the line x=2. Your answer
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On a dark night, two ships, Saga and Hero, sail parallel to a straight coastline on which there are two lights of equal brightness, 16 kilometres apart. P(x, b) (-8, 0) (8, 0) x Suppose the coastline is represented by the x axis where the origin O is chosen to be the midpoint of the light sources. It is known that the (total) brightness from the lights on a ship at point P(x, b) is 1 I = b² +(x+8)² 'b² +(x-8)² + dI (i) Show that dx 2P where P= (x+8)(3² +(x – 8)*)* +(x -8)(s² +(x + 8)*)* | and Q = (3° +(x +8)*)} (s? +(x-87)'. To answer parts (ii) and (iii), you may assume the following factorisation, given by a computer package, that P= 2x(x² + 64 + b? +16/64 + b² (x² + 64 + b² –16/64 + b²). (ii) Saga sails parallel to the coast at a distance 15 km from the coast. dI show that, as Saga sails from left to right, the brightness By considering on Saga increases to a maximum when x= 0 and then decreases. dx (iii) Hero sails parallel to the coast at a distance 6 km from the coast. Describe…
Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y² − 6x − 2y² + 1 (Express numbers in exact form. Use symbolic notation and fractions where needed.) D(x, y): = Which of these points are saddle points? (-√2, 1) (-√2,0) (√2, -1) (√2,0) (-√2, -1) (√2, 1) Which of these points are local minima? (-√√2, -1) (√2, -1) (√2, 1) (-√2,0) (-√2, 1) (√2,0)

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