Partial Derivatives And Euler's Equation MCQ Level - 1

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

Again using the given condition

The correct answer is 

f₁ is homogeneous of degree 1 and f₂ 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: 

We σw/σx=1+e^xcos y

Integrate both w.r.t.x

w(x,y)  =x+e^x cosy+f(y)

σw/σy=0-e^xsiny+f’(y)

Given =-e^xsiny+2y

So,on comparing the above two equation

f’(y)=2y

f(y)=y2+c(on integration)

so, w(x,y)=x+e^xcos y+y²+c

Now, using (In2,0)is In2,we get

C=-2

Hence, w(x,y)=x+y²+e^xcosy-2

The correct answer is, option C; w=x+y²+e^xcosy-2

So, by Euler's theorem

The correct answer is: 2 tan u

So, 
2y = 4
y = 2
The correct answer is: y = 2