Advertisements
Advertisements
Question
In the following, determine whether the following function is homogeneous or not. If it is so, find the degree.
g(x, y, z) = `sqrt(3x^2+ 5y^2+z^2)/(4x + 7y)`
Solution
g(x, y, z) = `sqrt(3x^2+ 5y^2+z^2)/(4x + 7y)`
`"g"(lambdax, lambday, lambdaz) = sqrt(3lambda^2x^2 + 5lambda^2y^2 + lambda^2z^2)/(4lambdax + 7lambday)`
= `(lambdasqrt(3x^2 + 5y^2 + z^2))/(lambda(4x + 7y))`
= `lambda^circ "g"(x, y, z)`
Thus g is homogeneous with degree 0.
APPEARS IN
RELATED QUESTIONS
If w(x, y) = x3 – 3xy + 2y2, x, y ∈ R, find the linear approximation for w at (1, –1)
If u(x, y) = x2y + 3xy4, x = et and y = sin t, find `"du"/"dt"` and evaluate if at t = 0
If w(x, y, z) = x2 + y2 + z2, x = et, y = et sin t and z = et cos t, find `("d"w)/"dt"`
Let U(x, y, z) = xyz, x = e–t, y = e–t cos t, z – sin t, t ∈ R, find `"dU"/"dt"`
Let z(x, y) = x tan–1(xy), x = t², y = s et, s, t ∈ R. Find `(delz)/(del"s")` and `(delz)/(del"t")` at s = t = 1
W(x, y, z) = xy + yz + zx, x = u – v, y = uv, z = u + v, u, v ∈ R. Find `(del"W")/(del"u"), (del"W")/(del"v")` and evaluate them at `(1/2, 1)`
In the following, determine whether the following function is homogeneous or not. If it is so, find the degree.
h(x, y) = `(6x^3y^2 - piy^5 + 9x^4y)/(2020x^2 + 2019y^2)`
In the following, determine whether the following function is homogeneous or not. If it is so, find the degree.
U(x, y, z) = `xy + sin((y^2 - 2z^2)/(xy))`
If `"u"(x , y) = (x^2 + y^2)/sqrt(x + y)`, prove that `x (del"v")/(delx) + y (del"u")/(dely) = 3/2 "u"`
If v(x, y) = `log((x^2 + y^2)/(x + y))`, prove that `x (del"v")/(delx) + y (del"u")/(dely) = 1`
If w(x, y, z) = `log((5x^3y^4 + 7y^2xz^4 - 75y^3zz^4)/(x^2 + y^2))`, find `x (del"w")/(delx) + y (del"w")/(dely) + z (del"w")/(delz)`
Choose the correct alternative:
If w(x, y) = xy, x > 0, then `(del"w")/(delx)` is equal to
Choose the correct alternative:
f u(x, y) = x2 + 3xy + y – 2019, then `(delu)/(delx) "|"_(((4 , - 5)))` is equal to
Choose the correct alternative:
If w(x, y, z) = x2(y – z) + y2(z – x)+ z2(x – y) then `(del"w")/(delz) + (del"w")/(dely) + (del"w")/(delz)` is
