Find the Taylor polynomial T4 (x) of
order 3 for the function y=lnx at the point x0=4.
Write down the Taylor's formula for this function with R4 (x).
Find the MacLaurin polynomial of order 4 for the function y=ln(1+x).
Write down the MacLaurin's formula for this function with R5(x). Estimate the error of approximation of ln(1,3)
by T0 (0,3), where T0 is MacLaurin
polynomial of order 4 of the function y=ln(1+x).
Write down the Taylor's formula with the remainder of order 3 for
the function f (x) = 1/x1/2 at the point x0=1. Estimate the error of approximation of f (11/10) by T1 (11/10),
where T1 is Taylor polynomial of order 2 at the
point x0=1.
Write down the Taylor's formula with R3 (x) for
the function f (x)=x1/3 at the point x0=64.
Estimate the error of approximation of
Find the MacLaurin polynomial of order 4 for the function f (x)=sinx
and estimate the accuracy of the approximate formula sinx ≈
T0 (x) for ⎪x⎪
≤
p/6.
Using MacLaurin expansion of elementary functions find Taylor
series of the following functions at a given point:
Using the Newton's method find an approximate value of the root
of the equation f (x) = 0 from the interval [a, b] (in
3 steps). Show that this method can be applied.
