Question

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

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

Find the Taylor Series at a=pi/2 for f(x)=5cos(x).

Find the Taylor series for f(x) centered at
the given value of a. [Assume that f has a power
series expansion. Do not show that
Rn(x) → 0.]
f(x) = sin(x), a = pi/2

1) find the Taylor series expansion of
f(x)=ln(x) center at 2 first then find its associated radius of
convergence.
2) Find the radius of convergence and interval
of convergence of the series Σ (x^n)/(2n-1) upper infinity lower
n=1

How to find the first three terms of the Maclaurin Series for
f(x) = sin(2*pi*x).

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...

Find the Taylor series for f(x)= sinx at a=pi/6. (Find up to the
fifth degree)

Calculate the Fourier Series S(x) of f(x) = sin(x/2), -pi < x
< pi. What is S(pi) = ?

Find the Fourier series of the function:
f(x) =
{0, -pi < x < 0
{1, 0 <= x < pi

Problem 15:
Find the taylor series for f (x) = cos (2x) around x = pi/4, and
find its interval and radius of convergence.

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