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then the value of x^{2}f_{xx} + 2xyf_{xy} + y^{2}f_{yy} =
The correct answer is: 0
If u(x, y) = e^{αx+βy} satisfy the condition u_{xx}  7u_{xy} + 12u_{yy} = 0. α^{2}  7αβ + β^{2} = ____
We are given with u(x,y)=e^{α}^{x+}^{ }^{βy}
u_{x}=αe^{αx+ βy} , uy= βe^{αx+ βy}
u_{xx}=α^{2}e^{αx+ βy }, u_{yy}=β^{2}e^{αx+ βy}
u_{xy}= αβe^{αx+ βy}
put these values in the given relation, we get
u_{xx}7u_{xy}+12u_{yy}=0
e^{αx+ βy}[α^{2}7αβ+12β^{2}]=0
e^{αx+ β} ≠0=> α^{2}7αβ+12β^{2}=0
The correct answer is: 0
Let f = y^{x}, what is at x = 2, y = 1
f = y^{x}
The correct answer is: 1
If z = 2(ax + by)^{2} – (x^{2} + y^{2}) and a^{2} + b^{2} = 1 then find the value of
Correct Answer : 0
Explanation : dz/dx = 4a(ax+by)  2x
d^{2}z/dx^{2} = 4a^{2}  2
dz/dy = 4b(ax+by)  2y
d2z/dy2 = 4b^{2}  2
d^{2}z/dx^{2 }+ d^{2}z/dx^{2} = 4a^{2}  2 + 4b^{2}  2
=> 4(a^{2}+b^{2})  4
As we know that a^{2} + b^{2} = 1
=> 4(1)  4
=> 0
v is homogeneous function of degree 3
The correct answer is: 3
If u = log(tan x + tan y + tan z), then (sin 2x) u_{x} + (sin 2y)u_{y} + sin 2z)u_{z} is equal to
The correct answer is: 2
1 – 12 = –11
The correct answer is: 0
If w = x^{2}cos xy, then Find the value of a + b.
We have
= 1  0 = 1
a + b = 1
The correct answer is: 1
If v = log(x^{2} + y^{2}) then v_{xx} + v_{yy} equal to
The correct answer is: 0
If z = e^{a}^{x+by} f(ax  by) then the value of The value of n is
= 2abz
The correct answer is: 2
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