Question

1.

Use a deﬁnition of a Taylor polynomial to ﬁnd the Taylor
polynomial T2(x) for f(x) = x^3/2 centered at a = 4.

We use T1(3.98) to approximate (3.98)^3/2. Apply Taylor’s inequality on the interval [3.98,4.02] to answer the following question: can we guarantee that the error |(3.98)^3/2 −T1(3.98)| of our approximation is less than 0.0001 ?

Answer #1

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.

Let f(x) = 1 + x − x2 +ex-1.
(a) Find the second Taylor polynomial T2(x) for f(x)
based at b = 1.
b) Find (and justify) an error bound for |f(x) − T2(x)| on the
interval
[0.9, 1.1]. The f(x) - T2(x) is absolute value.
Please answer both questions cause it will be hard to post them
separately.

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

1.
Find the Taylor polynomial, degree 4, T4, about 1/2 for f (x) = tan-inv (x) and use it to approximate tan-inv (1/16).
2.
Find the taylor polynomial, degree 4, S4, about 0 for f (x) = tan-inv (x) and use it to approximate tan-inv (1/16).
3.
who provides the best approximation, S4 or T4? Prove it.

Let f(x) =(x)^3/2 (a) Find the second Taylor polynomial T2(x)
based at b = 1. x3. (b) Find an upper bound for |T2(x)−f(x)| on the
interval [1−a,1+a]. Assume 0 < a < 1. Your answer should be
in terms of a. (c) Find a value of a such that 0 < a < 1 and
|T2(x)−f(x)| ≤ 0.004 for all x in [1−a,1+a].

approximate the function f(x)= 1/sqrt(x) by a taylor polynomial
with degree 2 and center a=4. how accurate is this approximation on
the interval 3.5<x<4.5?

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)

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 ?

i) Approximate the function f(x) = cos x by a Taylor polynomial
of degree 3 at a = π/3
ii) What is the maximum error when π/6 ≤ x ≤ π/2? (this is the
continuation of part i))

The second-order Taylor polynomial fort he functions f(x)=√1+x
about X0= is P2=1+(x/2)-(x^2/2) using the given Taylor polynomial
approximate f(0.05) with 2 digits rounding and the find the
relative error of the obtained value (Note f(0.05=1.0247). write
down the answer and all the calculations steps in the text
filed.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 15 minutes ago

asked 23 minutes ago

asked 41 minutes ago

asked 54 minutes ago

asked 55 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago