Calc Review Jeopardy

Limits

100

Lim x approaches 5 ((x+10)/(x^2-100))

-1/5

200

Lim x approaches 2 ((2x-2)/(x-2))

DNE

300

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

0

400

Lim x approaches 0 ((sin^2(4x))/(x^2cos(2x)))

16

500

Lim x approaches b ((4a^2-x^2)/(2a+x))

2a-b

Derivatives

100

y=7/2x^3

-21/2x^4

200

y=5/8x^-3

15/8x^4

300

y=cbrt(x)+3

1/(3cbrt(x^2))

400

y=4/x^2+1/x^3

(-8x+3)/x^4

500

y=6/sqrt(4x)-3/x^2

-3/(2xsqrt(x))+6/x^3

Differentiation Rules

100

d/dx(c)=0

A constant

200

d/dx(x^n)=nx^(n-1)

Power Rule

300

d/dx[f(x)g(x)]=f(x)g’(x)+g(x)f’(x)

Product Rule

400

d/dx[f(x)/g(x)]=(g(x)f’(x)-f(x)g’(x))/g(x)]^2

 Quotient Rule

500

d/dx f(g(x))= f’(g(x))g’(x)

Chain Rule

Related Rates

100

Water leaks into a circular pool. The radius of the pool is increasing at a rate of 4 cm/min. How fast is the area of the pool increasing when the radius is 5 cm?

40pi cm^2/min

200

Find the rate of change of the area A, of a circle with respect to its circumference C.

C/2pi

300

A conical cup is 4cm across and 6 cm deep. Water leaks out of the bottom at the rate of 2cm^3/sec. How fast is the water level dropping when the height of the water is 3 cm.

-2/pi cm/s

400

The radius of a right circular cylinder is increasing at the rate of 4 cm/sec but its total surface area remains constant at 600cm^2. At what rate is the height changing when the radius is 10 cm.

-16cm/s

500

In a right triangle, leg x is increasing at the rate of 2 m/s while leg y is decreasing so that the area of the triangle is always equal to 6 m^2. How fast is the hypotenuse changing when x=3 m.

-14/15 m/s

Integrals

100

Int (5x+ 7)dx

(5x^2)/2+7x+C

200

Int 0 to 1 (5x)dx

5/2

300

Int -3 to 3 (2v^2/3)dv

12

400

Int ((t^2+2)^2/t^4)dt

x-4/x-4/(3x^3)+C

500

Int e to 2e (cosx - 1/x)dx

sin(2e)-ln(2)-sin(e)