Calculus Jeopardy

Derivatives

100

3x⁶

18x⁵

200

15x²+2x

30x+2

300

-sin(3x)

-3cos(3x)

400

Ln(3x³)

3/x

500

Cos(3x²+5x+3)

-Sin(3x²+5x+3)*(6x+5)

Integrals

100

∫x²dx

x³/3+C

200

∫-cos(x)dx

-sin(x)+C

300

∫3e^3xdx

e^3x+C

400

∫2x(x²+1)³dx

((x²+1)⁴/2)+C

500

∫5x/(x²+4)

5/2ln(x²+4)+C

L’Hopital

100

lim_x->0(sin(x)/x)

1

200

lim_x->0(1-cos(x))/x²

1/2

300

lim_x->1(x³-1)/(x-1)

3

400

lim_x->0(e^x-1-x)/x²

1/2

500

lim_x->0(1-cos(2x))/x²

2

Product/Quotient Rule

100

2x²*5x-x

24x²

200

x²*sin(x)

2xsin(x)+x²cos(x)

300

x/(x+1)

1/(x+1)²

400

x²*ln(x)

2xln(x)+x

500

x³*cos(x²)

3x²*cos(x²)-2x⁴*sin(x²)

Average Value

100

Find the average value of x³ from [-1,2]

5/4

200

Find the average value of 1/x³ from [1,2]

3/8

300

Find the average value of √x from [0,4]

4/3

400

Find the average value of sin(x) from [0,π]

2/π

500

Find the average value of √(1-x²) from [-1,1]

π/4