Advertisements
Advertisements
Question
Choose the correct alternative:
If f(x, y) = exy, then `(del^2"f")/(delxdely)` is equal to
Options
xy exy
(1 + xy)exy
(1 + y) exy
(1 + x)exy
Solution
(1 + xy)exy
APPEARS IN
RELATED QUESTIONS
If w(x, y) = x3 – 3xy + 2y2, x, y ∈ R, find the linear approximation for w at (1, –1)
Let u(x, y, z) = xy2z3 x = sin t, y = cos t, z = 1 + e2t, Find `"du"/"dt"`
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
Let z(x, y) = x3 – 3x2y3 where x = set, y = se–t, s, t ∈ R. Find `(delz)/(del"s")` and `(delz)/(delt)`
In the following, determine whether the following function is homogeneous or not. If it is so, find the degree.
f(x, y) = x2y + 6x3 + 7
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))`
Prove that f(x, y) = x3 – 2x2y + 3xy2 + y3 is homogeneous. What is the degree? Verify Euler’s Theorem for f
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 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
