AP Calculus Jeopardy Game

Derivatives

100

The derivative is the ___ of the ___ at a ___; also known as the ______ rate of change.

slope; tangent line; point; instantaneous

200

Find the derivative of y=ln(x²)+3x^-2

Simplify your answer

y'=2/x-6x^-3

300

Write the equation of the line tangent to y=3x²+4x at (1, 7)

y-7=10(x-1)

400

Given f(3)=6, h(3)=2, h'(6)=4, h'(3)=15, and f'(3)=9. If g(x)=h(x)/f(x), find g'(3)

2

500

Given g(x)=h(f(x)) and f(3)=6, h(3)=2, h'(6)=4, h'(3)=15, and f'(3)=8; find g'(3).

32

Integrals

100

What is the antiderivative of 6x+e^x?

3x²+e^x+C

200

Find f(x) if f'(x)=2x and f(0)=5

f(x)=x²+5

300

The function f is continuous on the closed interval [2, 8] and has values given in the table. Using the intervals [2, 5], [5, 7], [7, 8] what is the left-hand Riemann sum for the integral from 2 to 8 of f(x)?

x      2   5   7   8

f(x) 20 30 40 10

160

400

Integrate 25x³-12x²+x

(25/4)x⁴-4x³+(1/2)x²+C

500

Given v(t), how can we find average velocity on the interval [a, b]?

1/(b-a) * integral (v(t), dt, from a to b)

Area/Vol.

100

This curve is closest to the x-axis when finding areas with more than one curve.

What is a minor curve?

200

A known __________ of A(x) can be used to find a volume of a solid. Fill in the blank..

What is a cross section?

300

Find the area enclosed by y=x² and the x-axis between x=0 and x=3

9

400

The inside of a funnel has a radius given by r=(1/20)(3+h²) from h=0 to h=10. Find the VOLUME of the funnel.

2209pi/40

500

Find the area enclosed by the graph of y=sqrt(x) and y=x².

1/3

Limits

100

Name the 3 of rules of continuity at x=c?

1) f(c) exists

2) lim x->c of f(x) exists

3) lim x->c of f(x)=f(c)

200

What Rule can be used for limits that result in 0/0 or infinity/infinity

L'Hopital's Rule

300

DAILY DOUBLE

Evaluate the limit of (x²-3x-10)/(x²-25) as x approaches 5

7/10

400

If the graph of y=(ax+b)/(x+c) has a horizontal asymptote at y=2 and a vertical asymptote at x=-3, then what is the value of a+c?

5

500

Find the constant a that makes the piecewise function f(x) continuous:

f(x)= 

{x²-2x+3 for x<=1

{ax²+4x-2 for x>1

0

Misc.

100

Find the derivative of 3y²+6=-7x

dy/dx=-7/(6y)

200

Find d²y/dx² of the following equation y=3x⁴-4x^3/2

y''=36x²-3x^-1/2

300

A function fails to be differentiable if it has a....

(4 answers total)

discontinuity, corner, cusp or a vertical tangent

400

For the integral of (x(x²+3)⁴), if you choose u=x²+3, then the integral becomes...

integral(1/2*u⁴)du

500

The differential equation dq/dt=t²q-3q in separable form is

dq/q=(t²-3)dt