show that f: R^2->R^2 be f(x,y)= (cosx + cosy, sinx + siny).
show that f is...
show that f: R^2->R^2 be f(x,y)= (cosx + cosy, sinx + siny).
show that f is locally invertible near all points (a,b)such that
a-bis not = kpi where k in z and all other points have no local
inverse exists
2. (a)
Determine all first and second order partial derivatives of
f(x,y,z) = x2y3 sin(xz)
(b)...
2. (a)
Determine all first and second order partial derivatives of
f(x,y,z) = x2y3 sin(xz)
(b) Determine all first-order partial derivatives of
g(x,y,z)=u2y+x2v where u=exz,
v=sin(yz)
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the...
part 1)
Find the partial derivatives of the function
f(x,y)=xsin(7x^6y):
fx(x,y)=
fy(x,y)=
part 2)
Find the partial derivatives of the function
f(x,y)=x^6y^6/x^2+y^2
fx(x,y)=
fy(x,y)=
part 3)
Find all first- and second-order partial derivatives of the
function f(x,y)=2x^2y^2−2x^2+5y
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 4)
Find all first- and second-order partial derivatives of the
function f(x,y)=9ye^(3x)
fx(x,y)=
fy(x,y)=
fxx(x,y)=
fxy(x,y)=
fyy(x,y)=
part 5)
For the function given below, find the numbers (x,y) such that
fx(x,y)=0 and fy(x,y)=0
f(x,y)=6x^2+23y^2+23xy+4x−2
Answer: x= and...
a. Is F(x,y,z)= <(e^z)siny,(e^z)cosx,(e^x)siny> a
conservative vector field? Justify.
b. Is F incompressible? Explain. Is it...
a. Is F(x,y,z)= <(e^z)siny,(e^z)cosx,(e^x)siny> a
conservative vector field? Justify.
b. Is F incompressible? Explain. Is it irrotational?
Explain.
c. The vector field F(x,y,z)= < 6xy^2+e^z, 6yx^2
+zcos(y),sin(y)xe^z > is conservative. Find the potential
function f. That is, the function f such that ▽f=F. Use a
process.
Assume that all the given functions have continuous second-order
partial derivatives. If z = f(x, y),...
Assume that all the given functions have continuous second-order
partial derivatives. If z = f(x, y), where x = r2 + s2 and y = 6rs,
find ∂2z/∂r∂s. (Compare with Example 7.) ∂2z/∂r∂s = ∂2z/∂x2 +
∂2z/∂y2 + ∂2z/∂x∂y + ∂z/∂y
1. f(x, y, z) = 2x-1 − 3xyz2 + 2z/
x4
2. f(s, t) = e-bst...
1. f(x, y, z) = 2x-1 − 3xyz2 + 2z/
x4
2. f(s, t) = e-bst − a ln(s/t) {NOTE: it is
-bst2 }
Find the first and second order partial derivatives for question
1 and 2.
3. Let z = 4exy − 4/y and x =
2t3 , y = 8/t
Find dz/dt using the chain rule for question 3.