Question

find the 6th order taylor polynomial for f(x) = xsin(x^2) centered at a=0.

Answer #1

For the function f(x) = ln(4x), find the 3rd order Taylor
Polynomial centered at x = 2.

Find the Taylor series for f(x) =xsin(3x) centered at a=π/3 and
Find the radius of convergence of the series you found

Find the 4th degree, T4 taylor polynomial for f(x)=arctan (x)
centered at c=1/2 and use it to aproximate f(x)= arctan
(1/16)

Find the Taylor polynomial of degree 3, centered at a=4 for the
function f(x)= sqrt (x+4)

let f(x)=cos(x). Use the Taylor polynomial of degree 4
centered at a=0 to approximate f(pi/4)

Find the second degree polynomial of Taylor series for f(x)=
1/(lnx)^3 centered at c=2. Write step by step.

Find the degree 3 Taylor polynomial T3 (x) centered
at a = 4 of the function f(x) = (-7x+36)4/3

Let f(x) = 2/ x and a = 1. (a) Find the third order Taylor
polynomial, T3(x), that approximates f near a. (b) Estimate the
largest that |f(x)−T3(x)| can be on the interval [0.5,1.5] by using
Taylor’s inequality for the remainder.

1. This question is on the Taylor polynomial.
(a) Find the Taylor Polynomial p3(x) for f(x)= e^ x sin(x) about
the point a = 0.
(b) Bound the error |f(x) − p3(x)| using the Taylor Remainder
R3(x) on [−π/4, π/4].
(c) Let pn(x) be the Taylor Polynomial of degree n of f(x) =
cos(x) about a = 0. How large should n be so that |f(x) − pn(x)|
< 10^−5 for −π/4 ≤ x ≤ π/4 ?

PART A: Find the Taylor series for ln x
centered at x = 5
PART B: Find the second degree Taylor
polynomial for f (x) = arctan x centered at x = 0

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