Calculus Jeopardy

Limits

100

Lim x approaches 2 (2x-1)

3

200

Lim X approaches 2 ((2x-1)/(x-4))

-1.5

300

Lim x approaches infinity ((sin(2x))/x^2)

0

400

Lim x approach 4 ((sqrt(x)-2)/(x-4))

1/4

500

Lim x approach 1 ((2x-3)(sqrt(x)-1)/2x^2+x-3))

-1/10

Derivatives

100

y=2x^6

y'=12x^5

200

y=(x^3+1)^2

6x^5+6x^2

300

y=(x^2-3)/x^2+15)

6/x^3

400

y=x^2/sqrt(x+4)

3x^2+16x/2sqrt(x+4)(x+4)

500

y=cos(2x+4)^2

-2sin(4x+8)

Integrals

100

Int 5 dx

5x+C

200

Int 3x+1 dx 

3x^2/2+x+C

300

Int 0 to 5 15x dx

375/2

400

Int 1 to 2 1/(2x^2) dx

1/4

500

Int pi/2 to pi (sin^2(x)+15) dx

31pi/4

Anti-derivatives

100

2x^2

2/3x^3+C

200

2x^3+1/2x^2

1/2x^4+1/6x^3+C

300

(3x+2)^2

1/9(3x+2)^3+C

400

15x^2-x^3

5x^3-1/4x^4+C

500

sin(4x+15)^3+11cosx^2

-cos(4x+15)(3-cos^2(4x+15))/12+11C(x)+C

Differentiation Rules

100

Constant Rule

ddx(c)=0

200

power rule

ddx(x^n)=nx^n-1

300

product rule

ddx f(x)g(x)= f'(x)g(x)+g'(x)f(x)

400

quotient rule

ddx f(x)/g(x)= f'(x)g(x)-g'(x)f(x)/g(x)^2

500

Chain Rule

ddxf(g(x))=f'(g(x))g'(x)