Question

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

Answer #1

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,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.

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

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) = xe^sin(x^2y+xy^2) /(x^2 + x^2y^2 + y^4)^3 . Compute
∂f ∂x (√2,0) pointwise.

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.
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 ?? (?) Taylor polynomial of ? (?) = (? - ?) ?? (? - ?) centered on ?. Using the Taylor inequality, find the error of the approximation if .? ≤ ? - ? ≤ ?. ?.

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