A function that models the slope of the curve for all x-values for which it exists.
100
What does an integral function look like?
∫a^b f(x)dx
100
What is the mean value theorem?
f'(c)=[f(b)-f(a)]/b-a
100
What is a limit?
The value that a function approaches as the line approaches some point
100
What is the power rule for derivatives
What is A'b + B'a
200
How do derivatives and limits relate to each other?
The derivative measures the instantaneous rate of change of the function and is defined as the limit of the average rate of change in the function
200
pi
∫ (sin x+2)dx
0
2pi + 2
200
What is the rolle's theorem?
If f is continuous of a closed interval [a,b] and differentiable on that interval and f(a)=f(b) then there is a c in the interval [a,b] such that f'(c)=0
200
lim 100/(x^2+5)
x->inf.
0
200
What does an integral basically say?
Find the area under the curve of a line
300
4x^3 + 7x^2 + 2x + 3
12x^2 + 14x + x
300
What is an integral the opposite of?
A derivative
300
What is the first fundamental theorem of calculus?
That an indefinite integral of a function can be reversed by differentiation.
300
Lim x^2-3x-10/x^2-25
x->2
4/7
300
A function fails to be differentiable if it has a what?
A discontinuity, a hole, or an asymptote
400
Y=(3x+1)^2
18x+6
400
25x^3 - 12x^2 + X.
25x^4/4 - 4x^3 + x^2/2
400
What is the Disk Method?
All cross sections to find a volume will be in circle form, the formula for the cross section is A= pi r^2.