Question

The second-order Taylor polynomial fort he functions f(x)=xlnx about X0= 1 is P2= -1+(x-1)^2/2 using the given Taylor polynomial approximate f(1.05) with 2 digits rounding and the find the relative error of the obtained value (Note f(1.05=0.0512). write down the answer and all the calculations steps in the text filed.

Answer #1

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.

The second-order Taylor polynomial fort he functions
f(x)=x√x about X0= 1 is P2= -1/2+3x/2+3(x-1)^2/8
using the given Taylor polynomial approximate f(1.05) with 2 digits
rounding and the find the relative error of the obtained value
(Note f(0.05=1.0759). write down the answer and all the
calculations steps in the text filed.

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 ?

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.

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

approximate the value of ln(5.3) using fifth degree taylor
polynomial of the function f(x) = ln(x+2). Find the maximum error
of your estimate.
I'm trying to study for a test and would be grateful if you
could explain your steps.
Saw comment that a point was needed but this was all that was
provided

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.

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?

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. Find T5(x): Taylor polynomial of degree 5 of the function
f(x)=cos(x) at a=0.
T5(x)=
Using the Taylor Remainder Theorem, find all values of x
for which this approximation is within 0.00054 of the right answer.
Assume for simplicity that we limit ourselves to |x|≤1.
|x|≤ =
2. Use the appropriate substitutions to write down the first
four nonzero terms of the Maclaurin series for the binomial:
(1+7x)^1/4
The first nonzero term is:
The second nonzero term is:
The third...

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