Question

Find the first order Taylor polynomin of f(x,y)=x^2e^y at (0,0)

T1(x,y)=

Find the second orser Taylor polynomial of f(x,y)=x^2e^y at
(0,0)

T2(x,y)=

Answer #1

Let f(x,y)=2ex+y. Find the second-order Taylor polynomial for
f(x,y) at the point (0,0).
Group of answer choices
2+x+y+12x2+12y2
2x+2y+x2+y2
2+2x+2y+x2+2xy+y2
2−2x−2y+x2−xy+y2
None of the above.

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) =(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].

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).

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 ?

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.

Let f(x,y)=xcos(πy)−ysin(πx)f(x,y)=xcos(πy)−ysin(πx). Find the
second-order Taylor approximation for ff at the point (1, 2).

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.

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.

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