Calculus AB Jeopardy!

Limits

100

Find the limit as x approaches infinity: (x+18)/x³

0

200

Find the limit as x approaches infinity: (3x+7x²)/(12x²+2)

7/12

300

Find the limit as x approaches 2: (x²+x-6)/(x-2)(x+5)

5/7

400

Find the limit as x approaches 3: (x³-27)/(x-3)

27

500

Find the limit as x approaches 2: (x³-x²-4)/(3x²-x-10)

8/11

Derivatives

100

Derive f(x)= 4x³+7x²+3x+1

f'(x)= 12x²+14x+3

200

Derive f(x)= (2x+1)(x+2) Be sure to expand!

f'(x)= 4x+5

300

Derive f(x)= (3x²+2x)(5x³+x) Be sure to expand!

f'(x)= 75x⁴+40x³+9x²+4x

400

Derive f(x)= (2x²+7x)/(3x²+2)

f'(x)= (-21x²+8x+14)/(9x⁴+12x²+4)

500

Derive f(x)= cos³(x²+2)

f'(x)= -6xcos²(x²+2)sin(x²+2)

Antiderivatives/Integrals

100

∫3x²+2x+9 dx

x³+x²+9x+C

200

∫cos(3x)+1 dx

((sin(3x)+x)/3)+C

300

(0,5)∫4x²-3 dx

155/3

400

∫sin(2x)+e^5x dx

(-cos(2x)/2)+(e^5x/5)+C

500

(2,6)1/2∫xsec²(x²+1) dx

-6.385/2

Tan/Normal Line

100

Find the equation of the tan line on the curve y=x² at x=3

y-9=6(x-3)

200

Find the equation of the tan line on the curve y=sinx at x=π

y-0=1(x-π)

300

Find the equation of the normal line on the curve y=(3x-1)/(2x+1) at x=-3

y-2=-5(x+3)

400

Find the equation of the tan line on the curve 3xy+y²-7x²=-3x at the point (1,1)

y-1=(8/5)(x-1)

500

Find the equation of the normal line to the curve y=2^3x

y-8=(-1/16.64)(x-1)

Misc.

100

Find the limit as x approaches infinity: (3x⁴+x³+x²+x)/(3x³+4x⁴)

3/4

200

Find the equation of the line tangent to y=sqrt(x) at x=4

y-2=(1/4)(x-4)

300

Derive the function f(x)=(x-2)²(3x+1)

f'(x)=9x²-22x+8

400

5ft deep cylindrical pool filled at a rate of 3 gal³/min. If the pool has a radius of 12ft how is h changing when h=3 (V=πr²h)

3/144π ft/min

500

Initial condition: (3,1)

dy1/y=3x²+2x+3 dx

y=e^{x^(3)+x^(2)+3x-18}