AP Calculus AB: MLG Jeopardy

Integrals

100

Solve the indefinite integral ∫ x^3dx

x^4/4 + C

200

Solve the definite integral ∫ (3x+4)dx on the interval (0,6)

14

300

Integrate: ∫(3-x)^10dx

-(3-x)^11 /11 + C

400

Integrate: ∫(sinx + cosx)^2dx

x + sin^2x + C

Derivatives

100

f(x) = 231x^3

693x^2

200

f(x) = xsinx

xcosx + sinx

300

f(x) = (x+7)/((x-6)(x+2))

-(x^2+14x-16)/((x-6)^2(x+2)^2)

400

f(x) = ln(7x^(2)e^(x)sinx)

(2/x) + 1 + cotx

Limits

100

What is the limit as x approaches 3 of (5x^2-8x-13)/(x^2-5)?

What is 2

200

What is the limit as x approaches 2 of (3x^2-x-10)/(x^2-4)?

What is 11/4 or 2.75

300

What is the limit as x approaches 0 of sin(5x)/3x

What is 5/3 or 1.67

400

What is the limit as x approaches 0 of (cos(2x)-1)/(cosx-1)?

What is 4

Chad

100

True or false: Chads full first name is Chadwick

False

200

What college did Chad attend

UW Platteville

300

What state is Chad's wife from

Colorado

400

What is Chad's height

5 foot 4 inches

Random Math

100

State the product rule for: ab

a*b' + a'*b

200

When does a function fail to be differentiable? Name 3 of the 4 common ways. 

The function: jumps, has a cusp/corner, has a infinite discontinuity, if the derivative is infinite 

300

State the Intermediate Value Theorem

For any value L between f(a) and f(b), there's a value c in [a,b] for which f(c)=L 

400

State the Mean Value Theorem 

if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].