b) The function is to be tabulated at equispaced points in the interval [2, 3] using linear interpolation. Find the largest step size h that can be used so that the error
in magnitude.
हमें फ़ंक्शन \[ f(x) = \ln(1 + x) \] को [2,3] के बीच समान दूरी के बिंदुओं पर टेबल रूप में दर्शाना है, और यह पता लगाना है कि अधिकतम स्टेप साइज़ \( h \) क्या हो सकता है ताकि लीनियर ________ ______ ______ ______ _______ ___.
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c) Using the classical R-K method of calculate approximate solution of the IVP,
at
taking
and
Use extrapolation technique to improve the accuracy.
b) A table of values is to be constructed for the function given by
in the interval [1, 4] with equal step length. Determine the spacing h such that quadratic interpolation gives result with accuracy
a) Show that where
and
are the average and central differences operators, respectively.
Take 10 figure logarithm to bases 10 from to
by unit increment. Calculate the first derivative of
when
b) Find the number of positive and negative roots of the polynomial
Find
and
using synthetic division method.
a) Find the dominant eigenvalue and the corresponding eigenvector for the matrix
using five iterations of the power method and taking as the initial vector.
b) Find by Newton’s method the roots of the following equations correct to three places of decimals
i) near
ii)