Question

Use a 2nd order Taylor polynomial centered at x = 4 to approximate √4.001 You can leave your answer as the sum or difference of fractions.

Answer #1

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

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 ?

What is the 2nd order Taylor polynomial of the function f (x) =
sqrt(x) at point a = 4? Please solve it!!!

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

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

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

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

Find the Taylor degree 4 polynomial of ? (?) = −? ∗ ??? (?)
centered on 0 and find the interval
for which the approximation has a smaller error or than a.
???.

Use the Taylor Polynomial of degree 4 for ln(1 − 4?)to
approximate the value of ln(2)

(1 point) Find the degree 3 Taylor polynomial T3(x) centered
at a=4 of the function f(x)=(7x−20)4/3.
T3(x)=
? True False Cannot be determined The function f(x)=(7x−20)4/3
equals its third degree Taylor polynomial T3(x) centered at a=4.
Hint: Graph both of them. If it looks like they are equal, then do
the algebra.

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