AP Calc Review

Derivatives

100

cos(x)

-sin(x)

200

3x⁵-2x²-7

15x⁴-4x

300

(3x²-5x+1)²

4(6x-5)(3x²-5x+1)³

400

4x^(-1/2)

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

500

((x²+1)^1/2) /( x³+2)

(-2x⁴-3x²+2x)/((x²+1)^1/2)(x³+2)²⁾

Anti-derivatives

100

-sin(x)

Cos(x)+C

200

X⁵-X²

(1/6)X⁶-(1/3)X³+C

300

3x⁴-2x^(1/2)+5x^-2

(3/5)x⁵-(4/3)x^(3/2)-5x^-1+C

400

sin(3x)

-(1/3)cos(3x)+C

500

X²ln(x)

(X³/3)ln(x)-(X³/9) + C

Riemann Sums

100

Use a Right Riemann Sum with 4 equal subintervals to approximate the total number of cookies over the interval (1,4)

63 cookies 

200

 

Use a Left Riemann Sum with 4 subintervals to approximate y over the interval (-2,2)

-10

300

Use a trapezoidal sum to find the approximate value over the interval (-3,2)

-12.5

400

Use a right Riemann sum to approximate y over the interval (1,10)

92

500

Use a Trapezoidal sum to approximate g(x) over the interval (-1,3) 

9.5

Limits

100

Find the limit as x approaches -3 of (x²+4x+3)/(x²-3)

0

200

Find the limit as x approaches 0 of (1-cos(x))/x²

1/2

300

Find the limit as x approaches 2 of (x³-8)/(x-2)

12

400

Find the limit as x approaches infinity of (5x²-3x+1)/(2x²+7)

5/2

500

Find the limit as x approaches 0 of (e^x-1-x)/(x²)

1/2

Tangent Line

100

Find the equation of the line tangent to x²+1 at x=2

y=4x-3

200

Find the equation of the line tangent to x^(1/2) at x=9

y=(1/6)x+(3/2)

300

Find the equation of the line tangent to ln(x) at x=1

y=x-1

400

Find the equation of the line tangent to e^x at x=1

y=e(x-1)+e

500

Find the equation of the line tangent to sin(x) at x=pi/6

y-(1/2)=(3^1/2/2)(x-(pi/6))