Phillip D-AP Calculus Review Game

Differentiation

100

Find the derivative of f(x)=3x⁵ - 4x² + 5

15x⁴ - 8x

200

Find the derivative of 12x⁵+27x²-3x

60x⁴+54x-3

300

Find the derivative of f(x)=32x²+Ln(4-x²)

64x - (2x/4-x²)

400

Find the derivative of x²e^3x

2xe^3x+3x²e^3x

500

Find the derivative of f(x)=(2x+1)³(x-3)⁴

(24x²-24x+6)(x-3)⁴+4(2x-1)³(x-3)³

Integration

100

Integrate F'(x)= 4x³ + 6x

x⁴ + 3x² + C

200

Integrate F'(x)=12x²+7x³

4x³+7/4x⁴

300

Integrate: sin(4x)dx

-1/4 cos(4x) + C

400

Find the general solution to the differentiable equation dy/dx=x/y

y²-x²= C

500

Integrate: Ln(x)/x dx

1/2 (Ln(x))² + C

Trig Derivatives

100

Find the derivative of sin (x)

cos (x)

200

Find the derivative of cos (x)

-sin (x)

300

Find the derivative of csc (x)

-csc(x)cot(x)

400

Find the derivative of sec(x)

sec(x)tan(x)

500

Find the derivative of cot(x)

-csc²(x)

Integral Identities

100

Integrate: sec²x dx

tan x + C

200

Integrate: csc²x dx

-cot x + C

300

Integrate: 1/x dx

ln x + C

400

Integrate: log (x) dx

x log(x) - x + C

500

Integrate: dx/sqrt (a²-x²)

arcsin (x/a) + C

Limits

100

When does a limit exist?

When the left and right hand limits are the same

200

What rule is used when a limit equals 0/0?

L'Hopital's rule

300

What are three types of discontinuities in calculus?

Removable, Infinite, and Jump

400

Evaluate lim_x->1(Ln(x)/x²-1)

1/2

500

Evaluate: lim_x->∞(e^x/x³)

∞