Calculus Jeopardy

Limits

100

Lim x approaches 5 ((3x-1)/(x-7))

-7

200

Lim x approaches 7 ((x+21)/(x^2-70)) 

-4/3

300

Lim x approaches -3 ((9+6x)/(x^2+2))

-9/11

400

Lim x approaches 0 (x/(4-sqrt(x+16))

-8

500

Lim x approaches 0 ((sin^2(3x))/(x^2cos(x)))

9

Derivatives

100

y=3/4x^2

3x/2

200

y=(x^2+x-2)/x^3

(-x^2-2x+6)/x^4

300

y=(x^3) - sqrt(x)

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

400

y=sqrt(x)/(x+3)^2

-(3(x-1))/(2sqrtx(x+3)^3)

500

y=arctan(2x-3)

1/(2x^2-6x+5)

Antiderivatives

100

Int(7cos(x)-9sin(x))dx

7sin(x)+9cos(x)+C

200

Int (5/(t-3t^2))dt

7sin(x)+9cos(x)+C-5(ln |3t-1|-ln (3|t|)+C

300

Int 3/sqrt(8-x)dx

-6sqrt(8-x)+C

400

Int 0 to 1 arcsin(x)dx

pi/2-1

500

Int (8sin(x/3)dx

24cos(x/3)+C

Integrals

100

Int 16 dx

16x+C

200

Int 3x^5-2x+5x+10 dx

(x^6/2)-x^2+(5x^2/2)+10x+C

300

Int 0 to 1 (8x)dx

4

400

Int 1 to 4 (4/x^3) dx

15/8

500

Int -1 to 1 (3x^2-1)^3 dx

32/35

U-Substitution

100

Int (5x+2)^2 dx

u=5x+2

200

Int 4t^2(t^3+6)^4 dt

u=t^3+6

300

Int t^5(t^3+9)^-1/2 dt

u=t^3+9

400

Int cos(4x+3)dx

u=4x+3

500

Int sin(x)/(cos(x))^4 dx

u=cos(x)