# 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**