Limits and continuity
as x approaches 2, lim(3x+1)
7
Find derivative of y = x2
2x
If f(x)>0, the function is...
increasing
True or False: Related rates problems involve time
True
Evaluate integral of: 2xdx
x2+C
as x approaches 4, lim(x2-5)
11
Derivative of f(x)=4x3
12x2
if f(x)<0, the graph is
concave down
If a circle's radius increases, does its area increase?
Yes
Evaluate integral of 5dx
5x+C
Is f(x)=x2 continuous at x=3?
Yes
derivative of f(x) = 4x3
12x2
What are the critical points used to find?
Max and min
Formula for the area of a circle?
A = pir2
What does a definite integral represent?
Area under the curve
For continuity at x=a, what must equal f(a)
lim as x approaches a f(x)
f(x)=x2sin(x)
2xsin(x)+x2cos(x)
A rectangle with perimeter 20 has maximum area when its dimensions are...
5 by 5
If r=5 and Dr/dt =2, what is dA/dt
20pi
Evaluate integral from 0-2 of xdx
2
as x approaches 1, (x2-1)/(x-1)
2
f(x)=(x2+1)/x
(x2-1)/x2
An optimization problem seeks a:
A balloons radius is increasing. Which derivative measures how fast volume changes?
dV/dt
8