Calculus Jeopardy

Basic Derivatives

100

y'(x^4)=

What is y'=4x^3

200

y'(2^x)=

What is y'=ln(2)*2^x

300

y'(3x^2+5x)(e^x)=

y'=(3x^2+5x)e^x+(6x+5)e^x

400

y'((5x^8-2x^40)/(t^2))=

y'=(t^2(40x^7-80x^39)-(5x^8-2x^40)2t)/(t^4)

500

y'(5e^(2x-3)^3)=

y'=(30e^(2x-3)^3)*(2x-3)^2

Complex Derivatives

100

y'(lnx)=

y'=(1/x)

200

y'(cos(x))=

y'=(-sin(x))

300

y'(csc(x))=

y'=(-csc(x)*cot(x))

400

y'(arcsin(3))=

y'=(1/((-8)^(1/2)))

500

y'(arctan(4x^2))=

y'=x/(1+2x^4)

Integrals

100

int(4)dx=

4x+c

200

int(7x^(2)+12x)=

(7/3)x^(3)+6x^(2)+c

300

int(13x^(3)+7x^(2)-2x-21)dx=

(13/4)x^(4)+(7/3)x^(3)-x^(2)-21x+c

400

int((3/x)+e^(x)+4x^(5))

3ln(x)+e^(x)+(2/3)x^(6)+c

500

int((1/x^(4))+4e^(4x)+2x^(1/2)

(-1/3)x^(-3)+e^(4x)+(4/3)x^(3/2)+c

Complex Integrals

100

int(3x^(2)*cos(x^(3))dx)=

sin(x^(3))+c

200

int(4sin(x)cos(x)dx)=

2sin^(2)(x)

300

x^(2)sin(x)dx

-x^(2)cos(x)+2(xsin(x)+cos(x))+C

400

int(e^(x)sin(x)dx=

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

500

int((sin(x))^(2)dx=

((-cos(x)sin(x)+x)/2)+C

Mathematicians

100

Who was the first person to apply calculus to general physics?

Newton

200

Who came up with an easy way to algebraically approximate the area under a curve?

Bernhard Riemann

300

What famous mathematician discovered a rule that uses derivatives to evaluate limits involving indeterminate forms?

Guillaume de l'Hôpital

400

Which mathematician discovered the method that uses midpoint approximation and trapezoid approximation to give a more accurate approximation for the area under a curve?

Thomas Simpson

500

Who's the best math teacher in all of history?

Higgie