Ap Calc

Vocab

100

What is the mathematical term for a true mathematical statement ?

Theorem 

200

What is the mathematical term for the reverse operation of derivatives ? 

Integral 

300

What is the formula for finding the derivatives of a composition of functions ?

Chain rule

400

What is a number that is equal to the exponent on a given base that would give that number ?

Logarithm 

500

What is a certain kind of visualization of a differential equation ?

Slope field

Limits

100

Evaluate the limit as x approaches -3 of 6+4x/x²+1

-3/5

200

What is the limit as x approaches 3 of x/x-3

DNE

300

What is the vertical asymptote of f(x)= x²+x-12/2x+8

-7/2

400

What is the limit as x approaches -3 of 3x(1/x+1/3)/3x(x+3)

-1/9

500

Fine the limit as x approaches pi

{^{cosx-sinx    When x is greater than or equal to pi             x-pi-1           X>pi}

-1

Related rates

100

A water tank in the shape of an inverted circular cone with base radius 2 meters and height 4 meters. If water is being pumped into the tank at a rate of 2m³/min, find the rate at which the water level is rising when the water inside is 3 meters deep. 

8/9pi m/min

200

A plane flying horizontally at an altitude of 1 mile and a speed of 500 miles/h passes directly above a station. Fine the rate at which the distance from the plane to the station is increasing when it’s 2 miles away from the station 

250/(radical 3)miles per hour

300

A spherical balloon is being inflated at a rate of 100 cm³/sec. How fast is the radius of the ballon increasing when the diameter is 50 cm ?

Dr/dt = 1/25pi cm/sec

400

A 400 pound stone dropped in a pond send a circular ripple whose radius increases at a constant rate of 4 ft/sec. After 12 seconds how rapidly is the area included by the ripple increasing?

384pi ft²/sec

500

A 500 13ft ladder is leaning against a wall when its base starts to slide away from the wall. By the time its base is 12ft from the wall, the base is moving at the rate of 5ft/sec. How fast is the top of the ladder sliding down the wall ?

-12ft/sec

Derivatives

100

Find h’(x)

H(x) = 3x⁷-6x⁴+8x³-12x+8

21x⁶-24x³+24x²-12

200

Find g^’(x) 

g(x) = (x²+1)(x²-2x)

4x³-6x²+2x-2

300

Find f’’(x) of 2=ln(7-x³)

-42x-3x⁴/(7-x³)²

400

Find f’(x) of 2xsin(x)+x²e^x

Xe^x(x+2)

500

F’’’(x) of 4x^3/5-1/8x^-2-x^1/2

168/126x^-17/5-15x^-6+15/16x^-7/2

Integral

100

Find the integral of (6+2y)dy

6y+y²+c

200

Find the integral of 3/x⁴

-x^-3+c

300

Find the integral of (2-1/x⁵+7/x³)

2x+x^-4/4-7/2x^-2+c

400

Find the integral of x³-4x-1/2x³

1/2x+2x^-1+1/4x^-2+c

500

f”(x)=2, f’(1)=4, f(1)=8 

Solve the differential equation with the given initial conditions

X²+2x+5