Calculate the third-degree Taylor polynomial about x0 = 0 for f(x) = (1 +x)1/2.
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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.
Using the following table of values, find approximately by Simpson’s rule, the arc length of the graph between the points (1 , 1) and
| x | 1 | 2 | 3 | 4 | 5 |
| 1.414 | 1.031 | 1.007 | 1.002 | 1.001 |
Using finite differences, show that the data
| x | − 3 | − 2 | − 1 | 0 | 1 | 2 | 3 |
| f ( x) | 13 | 7 | 3 | 1 | 1 | 3 | 7 |
Show that ux = c1eax + c2e-ax is a solution of the difference equation
ux+1 - 2ux cosh .
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.
Using of x0 = −2 as an initial approximation find an approximation to one of the zeros p(x) = 2x4 − 3x2 + 3x − 4 by using Birge-Vieta method. Perform two iterations.
Show that
where μ and are the average and central
differences operators, respectively.