Calcpardy

Limits and continuity

100

as x approaches 2, lim(3x+1)

7

200

as x approaches 4, lim(x²-5)

11

300

Is f(x)=x² continuous at x=3?

Yes

400

For continuity at x=a, what must equal f(a)

lim as x approaches a f(x)

500

as x approaches 1, (x²-1)/(x-1)

2

Derivatives

100

Find derivative of y = x²

2x

200

Derivative of f(x)=4x³

12x²

300

derivative of f(x) = 4x³

12x²

400

f(x)=x²sin(x)

2xsin(x)+x²cos(x)

500

f(x)=(x²+1)/x

(x²-1)/x²

Applications and optimization

100

If f(x)>0, the function is...

increasing

200

if f(x)<0, the graph is

concave down

300

What are the critical points used to find?

Max and min

400

A rectangle with perimeter 20 has maximum area when its dimensions are...

5 by 5

500

An optimization problem seeks a:

maximum or minimum value

Related rates

100

True or False: Related rates problems involve time

True

200

If a circle's radius increases, does its area increase?

Yes

300

Formula for the area of a circle?

A = pir²

400

If r=5 and Dr/dt =2, what is dA/dt

20pi

500

A balloons radius is increasing. Which derivative measures how fast volume changes?

dV/dt

Integrals and area under curves

100

Evaluate integral of: 2xdx

x²+C

200

Evaluate integral of 5dx

5x+C

300

What does a definite integral represent?

Area under the curve

400

Evaluate integral from 0-2 of xdx

2

500

Evaluate integral from 1-3 of 2xdx

8