Free Printable Functions of several variable

1.

If $x^2+y^2=25$ , then $\frac{\text{d}y}{\text{d}x}=$

a)

-x/y

b)

y/x

c)

-y/x

d)

x/y

2.

The Taylors expansion of first order of $f\left(x\right)=e^x\cos y$ about (0,0) is

a)

$1+x$

b)

$1+x-y$

c)

$1+x-\left(\frac{y^2}{2}\right)$

d)

$1+x-y\sin\left(0\right)$

3.

For $f\left(x,y\right)=x^2-y^2$ , the point (0,0) is

a)

Maximum

b)

Minimum

c)

Saddle point

d)

undeterminable

4.

Maximize $f\left(x,y,z\right)=xyz$ subject to $x+y+z=6$ . The maximum value occurs at

a)

(1,2,3)

b)

(2,2,2)

c)

(3,2,1)

d)

(0,3,3)

5.

If $x=r\cos\phi,\ y=r\sin\phi$ , then $J\left(\frac{x,y}{r,\phi}\right)$ is

a)

$r^2$

b)

0

c)

r

d)

-r

6.

If two functions are dependent, then their Jacobian is

a)

Positive

b)

Negative

c)

Zero

d)

Infinity

7.

The method of Lagrange multipliers is used to

a)

Approximate a function by series

b)

Find maxima/minima subject to a constraint

c)

Differentiate implicit functions

d)

Transform coordinates

8.

For a function $f\left(x,y\right)$ , a point $\left(x_0,y_0\right)$ is called a critical point if

a)

$f\left(x_0,y_0\right)=0$

b)

$f\left(x_0,y_0\right)$ is maximum only

c)

$f_x\left(x_0,y_0\right)=f_y\left(x_0,y_0\right)=0$

d)

The point lies on the x- axis

9.

The Taylor series expansion of a function of two variables $f\left(x,y\right)$ about $\left(a,b\right)$ is

a)

Expansion in powers of x and y only

b)

Expansion involving only linear terms

c)

A polynomial approximation without derivatives

d)

Expansion involving partial derivatives of $f$ at $\left(a,b\right)$

10.

The Jacobian of the inverse transformation satisfies the property

a)

$J\left(\frac{u,v\ }{x,y}\right)\times J\left(\frac{x,y\ }{u,v}\right)=0$

b)

$J\left(\frac{u,v\ }{x,y}\right)=J\left(\frac{x,y\ }{u,v}\right)$

c)

$J\left(\frac{u,v\ }{x,y}\right)=0$

d)

$J\left(\frac{u,v\ }{x,y}\right)\times J\left(\frac{x,y\ }{u,v}\right)=1$

Functions of several variable

Total questions: 10

Worksheet time: 5mins

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