What is the Fundamental Theorem of Calculus part 1
100
1. Find Domain. 2. Find Symmetry. 3. Do 1st and 2nd derivative tests. 4. Find critical points and candidates for critical points. 5. Determine increasing/decreasing and concavity. 6. Find extreme values and inflection points. 7. Determine asymptotes and end behavior. 8. Find intercepts. 9. Determine appropriate scale and plot function.
What is the steps for finding graphs of functions?
200
Let f(x) be a function defined for all x close to some point a.
lim(x-a)〖f(x)〗=L if the function values f(x) get closer and closer to L for all x that are sufficiently close to a.
What is the definition of a limit?
200
d/dx [f(x)g(x)]=f(x)g'(x)+f'(x)g(x)
What is the product rule?
200
x =a+(k-1)∆x
k
What are anchor points for a Left Reimann Sum?
200
b
∫f(x)dx=F(b)-F(a)
a
What is the Fundamental Theorem of Caluclus Part 2?
200
L(x)=f'(a)(x-a)+f(a)
What is linear approximation?
300
Let f(x) ≤ g(x) ≤ h(x) and all x be close to the same point a.
If lim(x-a)[f(x)]=L, then lim(x-a)[g(x)]=L also.
What is the squeeze theorem?
300
tan(Θ)sec(Θ)
What is the derivative of sec(Θ)?
300
x =a+(k-1/2)∆x
k
What are anchor points for midpoint Reimann Sum?
300
b _
(1/b-a)∫f(x)dx=f
a
What is Mean Value Theorem for Integrals?
300
If f is continuous on closed interval [a,b] and differentiable on open interval (a,b), then there is at least one point c such that f(b)-f(a)=f'(c)(b-a).
What is the Mean Value Theorem?
400
If the limit of f(x) as x goes to ±∞ is L, then the line y=L is...
What is a horizontal asymptote?
400
If f' changes from - to + at x=c, then f(c) is a maximum and from + to - is a minumum.
What is the first derivative test?
400
x =a+k∆x
k
What are anchor points for Right Reimann Sum?
400
f(-x)=-f(x), symetric about the origin
What is an odd function?
400
1. Understand the problem.
2. Identify the objective.
3. Determine the constraint.
4. Choose a single variable.
5. Express in terms of other variables.
6. Solve problem.
7. Does this make sense?
What are general guidelines to an optimization problem?
500
If the Lim f(x) = ±∞, then.....
x--a
What is a vertical asymptote?
500
1/√(1-x^2)
What is the derivative of sin^-1?
500
b-a/n
What is ∆x?
500
∫f(g(x))g'(x)=∫f(u)du
What is the subsitution rule for integrals?
500
If f(x) is continuous between two points, (a & b), any other point between two function values, (f(a) & f(b)), then f(x)=L has at least one solution between a & b.