Calc Project Jeopardy

Calculus in Music

100

The pitch of a note is referring to what part of the wave?

The frequency

200

What is the term used to refer to a tone with varying volume?

Amplitude modulation

300

What branch of mathematics is used to approximate piecewise waveforms using basic trigonometric functions?

Fourier analysis

400

What is the upper hull function of the following waveform:

t sin(2pi * 440t) + t² sin(2pi * 440t)

t + t²

500

Write the function for a sawtooth wave with frequency 520 Hz and an initial amplitude of 20 dB, given that the rate of change of A is 1 dB/s.

2(20 + t) mod(520t, 1) - (20 + t)

Derivatives

100

What is the derivative of 

11x² + 15x - 5/x

22x + 15 + 5/x²

200

What is the derivative of 

sin^-1(5x) + cos^-1(5x)

0

300

Find the points on the graph of x^5/2+ y^5/2= 1, where the slope of the tangent line is -1

y' = -x^3/2/ y^3/2

400

Find the derivative of y = (1/5)sec^-4(4 + x³)

(-12x²/5)sec^-4(4+x³)tan(4+x³)

500

What is the derivative of x^x (Must have a ln(x) in your answer)

(ln(x) + 1)x^x

Integrals

100

What is the integral of 10/x + 10/(x²)?

10ln(x) -10/x + C

200

What is the integral of (x²+4)/x²

x - 4/x + C

300

Find the integral of  1/(x^1/2(x+1)) 

2tan^-1(x^1/2) + C

400

Find the integral of x³e^{x^2}  

1/2(x²e^{x^2} - e^{x^2}) + C

500

Find the integral of 1/(x²-x+1)

(3*3^1/2/8)tan^-1(2/3^1/2(x-1/2)) + C

Series/limits

100

Which series converges as n approaches infinity

A) 5(1.4)ⁿ  B) 1/n^0.7  C) 300/n^1.5  D) 0.1(2.1)ⁿ

C) P-series

200

What converges conditionally as n approaches infinity

A) ((-1)ⁿ/n)   B) (1/n)  C) ((-1)ⁿ/n²)  D) 5

A) 

300

If a is a non zero number and r is a real number with 0<|r|,1 what is the value of 

((∞)sum(n=0) arⁿ) - ((∞)sum(n=1)arⁿ)?

a

400

Does the series eⁿn!/nⁿ as n approaches infinity:

Converge or Diverge

Diverges

500

find the limit as n approaches infinity of (n!)^1/n/n

e^-1

Random

100

Who was our fourth president?

James Madison

200

What's America's biggest state? (by size)

Alaska

300

All the following countries use the word "pan" to refer to bread except for...

A) Japan B) Spain  C) Germany D) Portugal

C) Germany

400

Are there more Wheels or doors? 

Wheel — Anything that can be thought of as a physical wheel is considered a wheel (wheels for transportation, toy wheels, wheels on appliances, shopping carts, wheels within machines, etc).

Door — Anything that can be thought of as a physical door is considered a door (car door, house door, cabinet door, locker door, etc).

Wheels

500

How many sides does a icosagon have?

20