Calculus Jeopardy Game

Theorems

100

Use product rule to find d/dx x(1 - 2/x)

1

200

Use product rule to find d/dx (2 - 3x)(x² + 5x - 1)

-9x² - 26x + 13

300

d/dx (3x+9/2-x)

15/(2-x)²

400

d/dx (x+4/2-3x)

14/(2-3x)²

500

d/dx (4x-7/x²+5x)

-4x²+14x+35/(x²+5x)²

Derivative

100

Find the derivative of f(x) = 4x³ + 8x² + 3x + 2

f'(x) = 12² + 16x + 3

200

d/dx (sin²(x))

sin(2x)

300

Find the derivative of f(x) = 6(cos(pix))³

f'(x) = -18pi*cos(pix)²sin(pix)

400

Find the derivative of f(x) = sqrt(6x³ + 5x² - 9)

x(9x + 5)/(6x³ + 5x² - 9)^1/2

500

d/dx (5x²+6x+9)/(2-x8)

5x²-40x-33/2(x-4)²

Limits

100

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

1

200

lim x->3  (5x² - 8x -13/x² - 5)

2

300

lim x-> infinity (7 + 8x + x^4/3)

infinity

400

lim (x,y) -> (3,3) (x-y/sqrt(x) - sqrt(y))

2sqrt(3)

500

lim x-> infinity (45.7563 + 74.2949e^-0.0363x)

45.7563

Area between curves

100

y = 6x + 8 and x = 5

361/3

200

y = x² + 3x + 9 and y = 0

65/6

300

y = x² + 7 and y = 1/3x + 18

397sqrt(397)/162

400

y = 3x, y = 3/5x, y = 28 - x²

8958/125

500

y = 6x²ln(x), y = 24ln(x)

2.847

Integrals

100

integral of cos³(x)sin(x) dx

-1/4cos⁴(x) + C

200

integral from 0 to pi sin(x)dx

2

300

integral (2x+1)/(x+5)³

2/x+5 + 9/2(x+5)² + C

400

integral from 0 to 2pi (cos²(theta)d(theta))

pi

500

integral of (5x²+7x+1)/(x+4)²

5x-33ln|x+4| - 53/x+4 + 20 + C