# Unit 1 (Maths 2)

## Quiz 1

If u=x^3+y^3 then [(∂^2)(u)]/∂x∂y is
3
-3
3x+3y
0

0

If u=F(y-z,z-x,x-y) then ∂u/∂x + ∂u/∂y + ∂u/∂z is equal to
1
2
3
0

For homogeneous function the linear combination of rates of independent change along x and y axes is __
Integral multiple of function value
no relation to function value
real multiple of function value
depends if the function is a polynomial

real multiple of function value

The total derivative is the same as the derivative of the function.
True
False

True

## Quiz 2

If u=xyF(y/x) then x∂u/∂x + y∂u/∂y=
u
2u
3u
4u

2u

A non-polynomial function can never agree with euler’s theorem.
True
False

False

To find the value of sin(9) the Taylor Series expansion should be expanded with center as _
9
8
7
Some delta (small) interval around 9

Some delta (small) interval around 9

If u=F(y-z,z-x,x-y) then ∂u/∂x + ∂u/∂y + ∂u/∂z is equal to
1
2
3
0

*pending

## Surpise Test

The existence of first order partial derivatives implies continuity.
True
False

False

A non-polynomial function can never agree with euler’s theorem.
True
False

False

Differentiation of function f(x,y,z) = Sin(x)Sin(y)Sin(z)-Cos(x) Cos(y) Cos(z) w.r.t ‘y’ is?
f’(x,y,z) = Cos(x)Cos(y)Sin(z) + Sin(x)Sin(y)Cos(z)
f’(x,y,z) = Sin(x)Cos(y)Sin(z) + Cos(x)Sin(y)Cos(z)
f’(x,y,z) = Cos(x)Cos(y)Cos(z) + Sin(x)Sin(y)Sin(z)
f’(x,y,z) = Sin(x)Sin(y)Sin(z) + Cos(x)Cos(y)Cos(z)

f’(x,y,z) = Sin(x)Cos(y)Sin(z) + Cos(x)Sin(y)Cos(z)

The total derivative is the same as the derivative of the function.
True
False

True

If u=e^(ax+by) then (∂^2u)/∂y∂x is
au
bu
abu
None of these

abu

For a homogeneous function if critical points exist the value at critical points is?
0
equal to its degree
1
-1

0

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