Question

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).

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.

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)=

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).

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.

) Consider the function f(x,y)=−2x^2−y^2.
Find the the directional derivative of ff at the point (1,−3)(1,−3)
in the direction given by the angle θ=π/2.
Find the unit vector which describes the direction in which ff
is increasing most rapidly at (1,−3).

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].

Find the quadratic approximation (Taylor Polynomial) for f(x,y)
= 2xe^(2y) near (2,0).

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) = 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.

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

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