CALCULUS JEOPARDY!

Derivatives

100

3x³ + 15x² - 7x - 3

9x² + 30x - 7

200

cos(2x) - sin(x²)

-2sin(2x) - 2xcos(x²)

300

12^{3x + 2}

12^{3x + 2} (3 ln|12|)

400

log₅x

1 / x ln (5)

500

e^-4x(sin3x)

3e^-4x (cos 3x) - 4e^-4x (sin 3x)

Integrals

100

integral 

(x² + 5x + 3) dx

(x³/3) + (5x²/2) + 3x + C

200

(tabular) integral of 

(x²(e^x))

x²(e^x) - 2x(e^x) + 2e^x + C

300

(division) integral of

(x² + 6) / (x + 1)

(x²/2) - x + 7 ln|x+1| + C

400

int. by parts 

e^x(cos(x)) 

(e^x (sin(x)+cos(x))) / 2

500

improper int. (from 0 to 4)

1/ sqrt. x

4

Parametric/Polar

100

parametric equations for

r = 5@    (x = ? , y = ?)

x = 5@(cos@), y = 5@(sin@)

200

set up arc length (from 1 to 3)

x(t) = t³ + 2    y(t) = 2t^9/2

(integral from 1 to 3) sqrt. (3t²)² + (9t^7/2)² dt

300

Set up arc length

r=6(sin@) 0<@<pi/2

3pi

400

find equation at t=1

x(t) = 3t²      Y(t) = 2t

Y - 2 = 1/3 (X - 3)

500

Polar coordinates.

Find dy/dx when r=e^@/5

5

Differentials

100

dy/dx = 4x - 2 

y = 2x² - 2x + C

200

dy/dx= y(sinx)

y=e if x=0

y= e^-cosx+2

300

dy/dx = e^{x + 3y}

y = -1/3 (ln (-3e^x - C)

400

dy/dx = e^{x - 9y}

y = 1/5 (ln (9e^x + C))

500

dy/dx = 4xe^3y

y = -1/3 (ln (-6x² + C))

Limits

100

limit as h -> 0

(x² + h) - (x²) / h

2x

200

limit as x -> 7 

(sqrt. (x + 2) - 3) / x - 7

1/12

300

limit as x -> 0

X²/(cosx - 1)

-2

400

limit as x -> 5

(x² - 25) / (x² - 4x - 5)

5/3

500

limit as x -> 0

(2^x + sinx) / x⁴

infinity !