Question

sin(x)=x-x^{3}/3!+x^{5}/5!

Below is the expansion of the Taylor series sin (x) function around the x = [x] point. Please continue.

Answer #1

Known f (x) = sin (2x)
a. Find the Taylor series expansion around x = pi / 2, up to 5
terms only.
b. Determine Maclaurin's series expansion, up to 4 terms only

Write an algorithm to calculate the sum of the following
series:
Sum
=x-x3/3! + x5/5! – x7/7!
+……. Stop when the term<0.0001.
very quick please.

Write the Taylor series for the function f(x) = x 3− 10x 2 +6,
using x = 3 as the point of expansion; that is, write a formula for
f(3 + h). Verify your result by bringing x = 3 + h directly into f
(x).

Find the first four terms in the Taylor series expansion of the
solution to
y′(x) = 2xy(x)−x3, y(0) = 1.

Find the Taylor series for the function f(x)=sin(pi(x)-pi/2)
with center a=1

Using the Taylor series for e^x, sin(x), and cos(x), prove that
e^ix = cos(x) + i sin(x) (Hint: plug in ix into the Taylor series
expansion for e^x . Then separate out the terms which have i in
them and the terms which do not.)

Consider the function ?(?) = sin(?). Find the Taylor series
formula when centered at ? = ?/3

For this problem, consider the function f(x) = ln(1 + x).
(a) Write the Taylor series expansion for f(x) based at b = 0. Give
your
final answer in Σ notation using one sigma sign. (You may use 4
basic Taylor
series in TN4 to find the Taylor series for f(x).)
(b) Find f(2020) (0).
Please answer both questions, cause it will be hard to post them
separately.

The hyperbolic cosine function, cosh x = (1/2) (e^x + e^-x).
Find the Taylor series representation for cosh x centered at x=0 by
using the well known Taylor series expansion of e^x. What is the
radius of convergence of the Taylor Expansion?

Calculus, Taylor series Consider the function f(x) = sin(x) x .
1. Compute limx→0 f(x) using l’Hˆopital’s rule. 2. Use Taylor’s
remainder theorem to get the same result: (a) Write down P1(x), the
first-order Taylor polynomial for sin(x) centered at a = 0. (b)
Write down an upper bound on the absolute value of the remainder
R1(x) = sin(x) − P1(x), using your knowledge about the derivatives
of sin(x). (c) Express f(x) as f(x) = P1(x) x + R1(x) x...

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