What is f(x)g'(x)+f'(x)g(x)
or
What is f'(x)g(x)+f(x)g'(x)
100
d/dx sin^-1x
The derivate of the arcsin(x)
1/(1-x^2)^.5
100
1/(b-a)∫f(x)dx integrated from a to b
What is the average value theorem
100
The 3 conditions that must occur for f(x) to be continuous at x=c
What is 1. f(c) exists
2. lim as x->c f(x)exists
3. lim as x->c f(x) = f(c)
200
d/dx(cosx)
What is -sinx
200
d/dx (f(x)/g(x))
What is
(f'(x)g(x)-f(x)g'(x))/(g(x)^2)
200
d/dx arccosx
What is -1/(1-x^2)^.5
200
There exists a point c in the interval (a,b) such that f'(c)=f(b)-f(a)/b-a, if a function is continuous on the closed interval [a,b] and differentiable on the open interval (a,b)?
What is the Mean Value Theorem.
200
The limit definition of the derivative of f(x): f'(x) =
What is lim h->0 (f(x+h)-f(x))/h
(or use (delta x) for h)
300
d/dx(tanx)
What is sec^2(x)
300
d/dx(f(g(x)))
What is
f'(g(x))*g'(x)
300
d/dx arctanx
What is 1/(1+x^2)
300
For the mean value theorem, these conditions must be met.
What is the function must be continuous and differentiable
(on the close interval [a,b] and open interval (a,b) respectively)
300
L'Hopital's rule for indeterminate limits states that if the limit as x->c (f(x)/g(x))=0/0 or ∞/∞
What is lim x->c f(x)/g(x) = lim x->c f'(x)/g'(x) if the new limit exists
400
d/dx(secx)
What is secxtanx
400
d/dx (e^x)
What is e^x
400
d/dx arccotx
What is -1/(1+x^2)
400
The average rate of change of a function f(x) on an interval [a,b]
What is (f(b)-f(a))/(b-a)
400
In terms of a graph, one that has a "hole" in it can be referred to as having this kind of discontinuity.
What is removable.
500
d/dx(cscx)
What is -cscxcotx
500
d/dx(b^x)
What is (b^x)lnb
500
Antiderivative of 1/(1+x^2)
What is arctanx + C
500
If f(x) is continuous on the closed interval [a,b], then for any k between f(a) and f(b), there exists c between a and b, such that f(c)=k
What is the Intermediate Value Theorem.
500
A discontinuity of a function at a point where the function has finite, but unequal, limits as the independent variable approaches the point from the left and from the right.