Quiz

This quiz is not graded. Check all applicable answers for multiple choice questions.

1.

What is a derivative of a function?

(a)

Difference of maximal and minimal values of the function

(b)

Slope of the tangent at a given point

(c)

$\lim_{\Delta x \to 0} \Delta y/\Delta x$

(d)

Speed of function's change

(e)

The lowest value of a function

2.

What is an integral?

(a)

Area under graphics of the function

(b)

Sum of the minimal and maximal value of the function

(c)

$\lim_{N\to\infty}\sum_{i=1}^N f(x_i)(x_{i+1}-x_i)$

(d)

$\lim_{N\to\infty}\sum_{i=1}^N f(x_i)$

(e)

The largest value of the function

3.

Area of a square with side a is a². Volume of a cube with the side a is a³. What is the volume of an N-dimensional hypercube with the side a?

4.

What is the probability to have a sum of three when throwing two dice? A sum of four?

5.

What is the dimension of the phase space for a system, that has only one particle moving along a straight line? Draw a trajectory in a phase space for a particle that has a constant velocity.

6.

What is the dimension for the phase space for a harmonic oscillator? Sketch its trajectory in the phase space.