- 3-220.127.116.11: Use Eq. (3.10) or Algorithm 3.2 to construct interpolating polynomi...
- 3-18.104.22.168: Use Eq. (3.17) or Algorithm 3.2 to construct interpolating polynomi...
- 3-22.214.171.124: Use the Newton forward-difference formula to construct interpolatin...
- 3-126.96.36.199: Use the Newton forward-difference formula to construct interpolatin...
- 3-188.8.131.52: Use the Newton backward-difference formula to construct interpolati...
- 3-184.108.40.206: Use the Newton backward-difference formula to construct interpolati...
- 3-220.127.116.11: a. Use Algorithm 3.2 to construct the interpolating polynomial of d...
- 3-18.104.22.168: a. Use Algorithm 3.2 to construct the interpolating polynomial of d...
- 3-22.214.171.124: a. Approximate f (0.05) using the following data and the Newton for...
- 3-126.96.36.199: how that the polynomial interpolating the following data has degree...
- 3-188.8.131.52: a. Show that the cubic polynomials P(x) = 3 2(x + 1) + 0(x + 1)(x) ...
- 3-184.108.40.206: A fourth-degree polynomial P(x) satisfies 4P(0) = 24, 3P(0) = 6, an...
- 3-220.127.116.11: The following data are given for a polynomial P(x) of unknown degre...
- 3-18.104.22.168: The following data are given for a polynomial P(x) of unknown degre...
- 3-22.214.171.124: The Newton forward divided-difference formula is used to approximat...
- 3-126.96.36.199: For a function f , the Newton divided-difference formula gives the ...
- 3-188.8.131.52: For a function f , the forward divided differences are given by x0 ...
- 3-184.108.40.206: a. The introduction to this chapter included a table listing the po...
- 3-220.127.116.11: Given Pn (x) = f [x0] + f [x0, x1](x x0) + a2(x x0)(x x1) + a3(x x0...
- 3-18.104.22.168: Show that f [x0, x1,... , xn , x] = f (n+1) ((x)) (n + 1)! , for so...
- 3-22.214.171.124: Let i0,i1,... ,in be a rearrangement of the integers 0, 1,... , n. ...
Solutions for Chapter 3-2: Divided Differences
Full solutions for Numerical Analysis (Available Titles CengageNOW) | 8th Edition
Angle of elevation
The acute angle formed by the line of sight (upward) and the horizontal
artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in three-dimensional space and ordered triples of real numbers
Boxplot (or box-and-whisker plot)
A graph that displays a five-number summary
The real number multiplied by the variable(s) in a polynomial term
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively
A ratio equal to 1, used for unit conversion
Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).
The numbers . . ., -3, -2, -1, 0,1,2,...2
Inverse cosine function
The function y = cos-1 x
kth term of a sequence
The kth expression in the sequence
The notation dy/dx for the derivative of ƒ.
nth power of a
The number with n factors of a , where n is the exponent and a is the base.
Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.
An annuity in which deposits are made at the same time interest is posted.
Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.
Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt
A matrix whose number of rows equals the number of columns.
Sum of a finite geometric series
Sn = a111 - r n 2 1 - r
Symmetric property of equality
If a = b, then b = a
Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.