English
Tamil Nadu Board of Secondary EducationHSC Science Class 12

In the following cases, determine whether the following function is homogeneous or not. If it is so, find the degree. f(x, y) = x2y + 6x3 + 7 - Mathematics

Advertisements
Advertisements

Question

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

Sum

Solution

f(λx, λy) = λ3x2y + 6λ3x3 + 7

There is no common λ in this equation.

∴ It is not homogeneous

shaalaa.com
Linear Approximation and Differential of a Function of Several Variables
  Is there an error in this question or solution?
Chapter 8: Differentials and Partial Derivatives - Exercise 8.7 [Page 86]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 12 TN Board
Chapter 8 Differentials and Partial Derivatives
Exercise 8.7 | Q 1. (i) | Page 86

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


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 = et 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 U(x, y) = ex sin y where x = st2, y = s2t, s, t ∈ R. Find `(del"U")/(del"s"), (del"u")/(del"t")` and evaluate them 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)`


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.

U(x, y, z) = `xy + sin((y^2 - 2z^2)/(xy))`


Prove that g(x, y) = `x log(y/x)` is homogeneous What is the degree? Verify Eulers Theorem for g


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`


Choose the correct alternative:

If f(x, y) = exy, then `(del^2"f")/(delxdely)` 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 f(x, y, z) = xy + yz + zx, then fx – fz is equal to


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×