Use the polynomial in part (i) to approximate
.
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Estimate the eigenvalues of the matrix
using the Gershgorin bounds. Draw a rough sketch of the region where the eigenvalues lie.
The position f (x) of a particle moving in a line at various times xk is given in the following table. Estimate the velocity and acceleration of the particle at x = 1.2.
| x | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 | 2.2 |
| f(x) | 2.72 | 3.32 | 4.06 | 4.96 | 6.05 | 7.39 | 9.02 |
Take 10 figure logarithm to bases 10 from x = 300 to x = 310 by unit increment. Calculate the first derivative of log10 x when x = 310.
Show that
where μ and are the average and central
differences operators, respectively.
Calculate the third-degree Taylor polynomial about x0 = 0 for f(x) = (1 +x)1/2.
Solve x3 − 9x + 1 = 0 for the root lying between 2 and 4 by the method of false position. Perform two iterations
A table of values is to be constructed for the function f (x) given by in the interval [1, 4] with equal step length. Determine the spacing h such that quadratic interpolation gives result with accuracy 1x10-6.