Question

Find the differential of f(x,y)=sqrt(x2+y3) at the point (2,3).

Then use the differential to estimate f(2.04,2.96).

Answer #1

-find the differential and linear approximation of f(x,y) =
sqrt(x^2+y^3) at the point (1,2)
-use tge differential to estimate f(1.04,1.98)

f(x,y) = x2 y – 4 x y3 + ex+ y
evaluate f(x,
x2) – f(1,1)
Define a saddle point in mathematical terms.

1. Find the differential of f(x,y)=\sqrt{x + e^{4y}}f(x,y)=
x+e^4y and use it to find the approximate change in the function
f(x,y)f(x,y) as (x,y)(x,y) changes from (3,0)(3,0) to
(2.6,0.1)(2.6,0.1).

F(x,y) = (x2+y3+xy,
x3-y2)
a) Find the linearization of F at the point (-1,-1)
b) Explain that F has an inverse function G defined in an area
of (1, −2) such that
that G (1, −2) = (−1, −1), and write down the linearization to G in
(1, −2)

Consider the function F(x, y, z) =x2/2−
y3/3 + z6/6 − 1.
(a) Find the gradient vector ∇F.
(b) Find a scalar equation and a vector parametric form for the
tangent plane to the surface F(x, y, z) = 0 at the point (1, −1,
1).
(c) Let x = s + t, y = st and z = et^2 . Use the multivariable
chain rule to find ∂F/∂s . Write your answer in terms of s and
t.

Show that the origin is a spiral point of the system
x' = -y - x(sqrt(x2 + y2))
y' = x - y(sqrt(x2 +
y2)) but a center for its linear approximation

Find the linear approximation of the function f(x, y, z) = sqrt
x2 + y2 + z2 at (3, 6, 6) and use it to approximate the number
sqrt3.01^2 + 5.97^2 + 5.98^2 . (Round your answer to five decimal
places.) f(3.01, 5.97, 5.98)

Find the absolute maximum value of the function
f(x,y)=x2-4xy+y3+4y on the triangular region
with vertices (-1,-1), (7,-1) and (7,7).

for the surface
f(x/y/z)=x3+3x2y2+y3+4xy-z2=0
find any vector that is normal to the surface at the point
Q(1,1,3). use this to find the equation of the tangent plane to the
surface at q.

Consider the following group of differential equations
y´+y=F(x), where
F(x)= x2, x3,...,xn
F(x)= sen x
F(x)= [x]
Resolve taking into account the above:
a. Find the solution for each of the differential equations
b. Discuss the trend approach between y (x) and f (x)
c. Describe characteristics of the pattern that constitutes the
expression of the solution y (x) and discuss it in the light of any
known method
Please help me to solve!

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