AP CALC BC REVIEW CYSD

Derivatives

100

sin(x)

cos(x)

200

tan^-1(x)

1/(x²+1)

300

(3x²+1)⁵

30x(3x²+1)⁴

400

sin(x²)/e^x

(e^x(2xcos(x²)-sin(x²)))/e^2x

500

-tan^-1(-540)

0

Integrals

100

2x

x²+C

200

16xsin(4x²+5)

-2cos(4x²+5)+C

300

(from -pi/2 to pi/2) 15sin(4x)

0

400

-2(5x⁴+3x²)cos(x⁵+x³)sin(x⁵+x³)

cos²(x⁵+x³)+C

500

6x/(4+9x⁴)

(1/2)tan^-1((3/2)x²)+C

Application of derivatives

100

Slope of the line y=5x at x=2

5

200

Slope of the line -2sin(x) at x=0

-2

300

What is the maximum area of an enclosure using 40 yards of fence

100 yrds²

400

What is the extrema for f(x)=2x-x²

(1,1)

500

A 13 foot ladder is leaning against a wall, if the top of the ladder slips down the wall at 2 feet per second how fast will the base of the ladder be moving away from the wall when the top of the ladder is 5 feet above the ground

5/6 ft/sec

Application of integrals

100

Area from x=1 to x=10 of y=8

72

200

displacement of car traveling 7t meters per second from t=0 to t=4

56

300

Area from the x axis to y=8 of 2x

16

400

Area between y=sec²x and y=sinx from x=0 to x=pi/4

(2)^1/2/2

500

Length of curve formula

int((1+(dy/dx)²)^1/2

Potluck

100

What was unit four of honors calculus

Applications of differentiation

200

There is no _____ in calculus

Crying

300

What is the mean value theorm formula

f^'(c)=(f(b)-f(a))/b-a

400

What veggie does mrs. Menges hate

green beans

500

First 4 nonzero terms of the maclaurin series for sin(x)

x-x³/3!+x⁵/5!