Question

Find the degree-2 Taylor polynomial for the function f(x, y) = exy at the point (4, 0).

Answer #1

(1 point) Find the degree 3 Taylor polynomial T3(x) of
function
f(x)=(7x+67)^(5/4)
at a=2
T3(x)=?

Let f(x, y) = sin x √y.
Find the Taylor polynomial of degree two of f(x, y) at (x, y) =
(0, 9).
Give an reasonable approximation of sin (0.1)√ 9.1 from the
Taylor polynomial of degree one of f(x, y) at (0, 9).

Find the Taylor polynomial of degree 4, p4(x), about 0 for the
function y = e^[x^(2)]. Find the precision for with which p4(x)
approximates e^[x^(2)], for values of x, -1/4 ≤ x ≤ 1/4.

(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.

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

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.

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 ?

Find the degree 3 Taylor polynomial T3(x) of function
f(x)=(7x−5)^3/2 at a=2. T3(x)=

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?

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