Calculus Jeopardy-Georgios Cosmas

Derivatives

100

What is the derivative of...

sin(x)?

cos(x)

200

What is the derivative of...

tan^-1(x)?

1/(x²+1)

300

What us the derivative of...

e^xsinx?

e^xcosx+(sinx)e^x

400

What is the derivative of...

(1-8x)^1/3?

In simplest form

(-8/3)(1-8x)^-2/3

500

What is the derivative of...

(sin^-1(-3x))+2x²?

In simplest form?

-3/(1-9x²)^1/2 + 4x

Integrals

100

What is the integral of...

-cos(x)?

-sin(x)+C

200

What is the integral of...

(2x-6)³?

In simplest form

(1/8)(2x-6)⁴+C

300

What is the integral of...

1/xlnx

In simplest form

ln|lnx|+C

400

What is the integral of...

e^2x/(1+e^2x)?

In simplest form

(1/2)(ln|1+e^2x|)+C

500

What is the integral of...

2/(x²+9)?

In simplest form

(2/3)(tan^-1(x/3))+C

Random

100

Evaluate lim_x→2(8−3x+12x²)?

50

200

Find the first five terms in the sequence...

{4n/n²−7}_n=0

{0, -2/3, -8/3, 6, 16/9}

300

Integration by parts...

 ∫ xe^x dx?

xe^x-e^x+C

400

Use ratio test the determine if it converges or diverges.

∑_n=1 3^1-2n/(n²+1)

Converges

500

Use root test the determine if it converges or diverges.

∑_n=1 (3n+1/(4n-2n))²ⁿ

Diverges

Mathematicians

100

What is the method that Michel Rolle is known for?

Rolle's Theorem

200

What is the method that Guillaume de l'Hôpital is known for?

L'hôpital's rule

300

What is the method that Leonhard Euler is known for?

Euler's Method

400

What is the method that Joseph-Louis Lagrange is known for?

Lagrange's Theorem

500

Sir Issac Newton and Gottfried Wilhelm Leibniz are both credited with what?

Discovering Calculus

Teachers

100

She is our AP Calculus teacher.

Mrs. Crawford

200

This teacher is head of the Math department.

Mr. Dods

300

She teaches only Introduction to BC Calculus Honors.

Mrs. Scala

400

She is one of the AP Statistics teachers.

Mrs. Getchell

500

He is one of the AP Statistics teachers.

Mr. Izzo