BC Calculus Jeopardy

Slippery Slopes

100

The derivative of 

e^{2x^2}.

What is 

4xe^{2x^2}?

200

The slope of the line tangent to  cos(pix) at x=0.5.

What is 

-pi?

300

The concavity of  f(x) = -x^3+2x^2-3x at x=1.

What is concave down?

400

lim_{x->0} frac{2x}{cosx-e^x}.

What is -2?

500

The slope of the constant polar function r=2 at  theta=pi/4.

What is -1?

Arduous Areas

100

int_0^1 3x^2+2x+4 dx

What is 6?

200

int frac{x+1}{x^2+2x}dx

What is 

1/2ln|x^2+2x|+C?

300

int frac{x+1}{x^2+x}dx

What is 

ln|x|+C?

400

int_0^2 \sqrt{4-x^2}dx

What is 

4pi?

500

int frac{x^2+2x-1}{x-4}dx

What is 

1/2x^2+6x+23ln|x-4|+C?

Serious Series

100

This test will determine the convergence of   sum_{n=2}^{oo} n .

What is the nth term (or limit divergence) test? Other possibilities: P-series (p=-1), integral test.

200

This test will help me determine the convergence of  sum_{n=1}^{oo} 1/{n^2-3} .

What is the limit comparison test?

300

The convergence type of  sum_{n=1}^{oo} (-1)^n/n . 

What is conditional convergence? (Daily double, what is the name of this series?)

400

The formula for the Lagrange Error Bound of a 4th degree Taylor Polynomial centered about x=1.

What is 

\frac{max(f^{(5)}(x))}{5!}(x-1)^5?

500

The radius of convergence for  sum_{n=1}^{oo} ({e^n}/{n!}x^n) .

What is 

oo?

Varying Variables

100

 frac{dy}{dx} if

y^2+2xy=1

What is 

-frac{y}{y+x}?

200

At the moment when the radius of a sphere ( V=4/3pir^3 ) is 5 feet, the volume of the sphere is increasing at a rate of  100pi feet/second. This is the rate at which the radius is increasing.

What is 1 foot/second?

300

 f(x)=4x^4+3x^2 and g is f's inverse. If g(1)=1, this is g'(1).

What is 22?

400

 {dw}/dx if  w=cosz , z=2y , and  y=e^{x^2} .

What is 

-4xe^{x^2}sin(2e^{x^2})?

500

If the velocity of a particle is given by  <3x^2+2, e^{3x}> , and the particle's position at t=0 is <1,1>, then this is the position of the particle at t=2.

What is 

<13,1/3e^6+2/3>?

Named After Me

100

This mathematician, frequently considered the father of calculus, is most widely known for his theory of gravitation.

Who is Sir Isaac Newton?

200

This mathematician, who invented the  dy/dx notation for derivatives, is best known for his feud with another important figure in the history of calculus.

Who is Wilhelm Gottfried Leibniz?

300

This Ancient Greek Mathematician, whose name features in an important fact relating to triangles, is also known for running a mathematical cult whose members abstained from eating beans.

Who is Pythagoras?

400

This mathematician, after whom a stepwise approximation method is named, has a name which is frequently mispronounced by calculus students.

Who is Leonhardt Euler?

500

This mathematician, whose greatest contribution to math was writing a textbook, is most famous for a technique named after him which he himself did not discover.

Who is Guillaume de L'Hospital?