Reference no: EM13888946
1. Use the Bisection method to find p3 for f (x) = √x - cos x on [0, 1].
2. Find an approximation to √3 correct to within 10-4 using the Bisection Algorithm. [Hint: Consider f(x) = x2 - 3.]
3. Let f(x) = x2 - 6 and p0 = 1. Use Newton's Method to find p2.
4. Let f(x) = x2 - 6 and p0 = 3 and p1 = 2, find p3
a) Use the Secant method.
b) Use the method of False Position
c) Which of a or b is closer to √6
5. Use Newton's method to find solutions accurate to within 10-5 to the following problem.
a) x2 - 2xe-x + e-2x = 0, for 0 ≤ x ≤ 1.
6. For the given functions f(x), let x0 = 1, x1 = 1.25, and x2 = 1.6. Construct interpolation polynomials of degree at most one and at most two to approximate f(1.4) and find the absolute error.
a) f(x) = sinπx
7. Determine the natural cubic spline S that interpolates the data f (0) = 0, f (1) = 1, and f (2) = 2.
8. Construct the natural cubic spline for the following data.
|
x
|
f(x)
|
|
8.3
|
17.56492
|
|
8.6
|
18.50515
|
9. What is the Taylor series of the function:
f(x) = x5 - 2x4 + 3x3 - 4x2 - 10x - 5 , at the point c =17.
|
Presentation on it project of office automation
: Working with each of the following (one Project Manager, one customer, others may be system architects/developers) to identify the system requirements and all risks. And, rate each risk.
|
|
What is a measure of operating leverage
: What is a measure of operating leverage, and how is it calculated? Pine Company has a degree of operating leverage of 8. Fir Company has a degree of operating leverage of 4. Interpret these measures.
|
|
Written pieces in a formal and logical manner
: Complete all written pieces in a formal and logical manner
|
|
Where the athenians unjust or justified in their conviction
: Essay question Where the Athenians unjust or justified in their conviction and condemnation to death of Socrates?
|
|
Construct interpolation polynomials of degree
: For the given functions f(x), let x0 = 1, x1 = 1.25, and x2 = 1.6. Construct interpolation polynomials of degree at most one and at most two to approximate f(1.4) and find the absolute error
|
|
Medieval universities differ from universities today
: Medieval Universities differ from universities today? See Jacques de Vitry's description of medieval students for one scholar's description of students in medieval universities.
|
|
What approach should be used to calculate break-even point
: What approach should be used to calculate the break- even point of a company that has many products? How is the contribution margin per unit of limited resource computed?
|
|
Paintings are often admired and studied for artistic reasons
: The authors of the course textbook state that "although paintings are often admired and studied for artistic reasons alone, their value as historical documents should not be overlooked. In an age before the camera, paintings, sketches, and even pictu..
|
|
How does sale mix affect the calculation of break-even point
: What is meant by term sales mix? How does sales mix affect the calculation of break-even point? If management chooses to reduce its selling price to match that of a competitor, how will the break-even point be affected?
|