Question

tan plane at (1,1)

v(j,k)= ln(10j^2 2k^2 + 1)

Answer #1

Let F(x, y, z) = z tan−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the
flux of F across S, the part of the paraboloid x^2 + y^2 + z = 29
that lies above the plane z = 4 and is oriented upward.

Find the position vector of a particle that has acceleration
2i+4tj+3t^2k, initial velocity v(0)=j+k and initial position
r(0)=j+k

Let f(x, y) = x tan(xy^2) + ln(2y). Find the equation of the
tangent plane at (π, 1⁄2).

Let F(x, y,
z) = z
tan−1(y2)i
+ z3
ln(x2 + 9)j +
zk. Find the flux of
F across S, the part of the paraboloid
x2 + y2 +
z = 7 that lies above the plane
z = 3 and is oriented upward.

Let F(x, y, z) = z tan−1(y2)i + z3 ln(x2 + 7)j + zk. Find the
flux of F across S, the part of the paraboloid x2 + y2 + z = 6 that
lies above the plane z = 5 and is oriented upward.

Let
F(x, y,
z) = z
tan−1(y2)i
+ z3
ln(x2 + 8)j +
zk.
Find the flux of F across S, the part
of the paraboloid
x2 +
y2 + z = 6
that lies above the plane
z = 5
and is oriented upward.
S
F · dS
=

Let f = sin(yz) + ln(x)
a) Find the derivative of F at P(1,1,Pi) in the direction of v =
i+j-k
b) Find a vector u in the direction where f increases the
fastest
c) Find a nonzero vector w with the property that the derivative
of f in the direction of w at P(1,1,pi) is 0

1. Prove that {2k+1: k ∈ Z}={2k+3 : k ∈ Z}
2. Prove/disprove: if p and q are prime numbers and p < q,
then 2p + q^2 is odd (Hint: all prime numbers greater than 2 are
odd)

Let ?(?, ?) = ??2 + ln(??).
1. Write the equation of the tangent plane to the surface at (1,
1).
2. If ?(?,?)=?^(2?+?) and ?(?,?)=?+?,find ??/?u
and ??/?v if ?=1 and ?=−2.
3. In what direction would ??⃑ (1, 1) be steepest? What is that
value?

Let F(x,y,z) = ztan-1(y^2) i + (z^3)ln(x^2 + 8) j + z k. Find
the flux of F across the part of the paraboloid x2 + y2 + z = 20
that lies above the plane z = 4 and is oriented upward.

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