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u and v are homogeneous function of degree one
on adding
The correct answer is: z
f(x, y) is homogeneous function of degree –2
So, using Euler's equation
The correct answer is: 0
If u = sin x/l*sin y/m * sin z/n * cospt satisfy the equation then
Again using the given condition
The correct answer is
f_{1} is homogeneous of degree 1 and f_{2} is homogeneous of degree zero
On adding
The correct answers are:
We have
u is homogeneous function of degree n
Now differentiate partially w.r.t. x again
The correct answer is:
Find a function w = f(x, y) whose first partial derivatives are and and whose value at point (ln2, 0) is ln2.
We σw/σx=1+e^{x}cos y
Integrate both w.r.t.x
w(x,y) =x+e^{x} cosy+f(y)
σw/σy=0e^{x}siny+f’(y)
Given =e^{x}siny+2y
So,on comparing the above two equation
f’(y)=2y
f(y)=y2+c(on integration)
so, w(x,y)=x+e^{x}cos y+y^{2}+c
Now, using (In2,0)is In2,we get
C=2
Hence, w(x,y)=x+y^{2}+e^{x}cosy2
The correct answer is, option C; w=x+y^{2}+e^{x}cosy2
If u = sin^{1} [(x^{3} + y^{3} + z^{3})/(ax + by + cz)] then xdu/dx + ydu/dy + zdu/dz equal to
So, by Euler's theorem
The correct answer is: 2 tan u
The contour on xy plane where partial derivative of x^{2} + y^{2} with respect to y is equal to the partial derivative of 6y + 4x w.r.t. x is
So,
2y = 4
y = 2
The correct answer is: y = 2
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