Calculus Jeopardy

Derivatives

100

f(x) = -7x - 9

Find f'(x)

f'(x) = -7

200

f(x) = 3cos(x/2 +5)

Find f'(x)

f'(x) = -(3sin(x/2 +5)/2

300

f(x) = 2ln(sin(x))

Find f'(x)

f'(x) = 2cos(x)/sin(x)

400

f(x) = tan^-1(4x² + 3x + 1)

Find f'(x)

f'(x) = (8x+3)/((4x²+3x+1)²+1)

500

f(x) = sin(ln(4x²-3x)

Find f"(x)

f"(x) = ((8x-3)cos(ln(4x²-3x)))/(4x²-3x)

Integrals

100

Find ∫(3x²)dx

What is x³ + C

200

Find ∫(1/x)dx

What is ln(x) +C

300

Find ∫(4x+sec²(x))dx

What is 2x² + tan(x) +C

400

Find ∫(cos(x) + e^x)dx

What is sin(x) +e^x +C

500

Find ∫(16/x⁵ + 9/x⁴ + 4/x³)dx 

What is -2/x² - 3/x³ - 4/x⁴ + C

Limits

100

lim(x→2)   (8-3x+12x²)

50

200

lim(x→infinity)  1/x

0

300

lim(x→0)   sin(x)/x

1

400

lim(x→1)  (x-1)/(sqrt(x²+3)-2)

2

500

lim(x→0)   (sqrt(x+2)+sqrt(x))/x

1/2sqrt(2)

Unit Circle

100

Find tan(π/4)

1

200

Find sin(π/3)

sqrt(3)/2

300

Find cos(5π/4)

What is -sqrt(2)/2

400

Find sin(7π/6)

What is -1/2

500

Find all values on [0,3π/2] of sin^-1(-sqrt(3π)/2

What is 4π/3

Logarithms

100

Find log₃9

What is 2

200

Find log₂8

What is 3

300

Find log_1/51/625

What is 4

400

Find ln e⁴

What is 4

500

Find log₀1

What is 0