Limits/Cont
This is the limit as x --> pi of sin(x).
What is 0?
This is the limit form of the derivative -- "when mom calls you by your full name"
What is [the lim as h --> 0 stuff. if i want to put fractions i have to pay this company $20 and i'm not gonna do that out of principle. sorry]
This is the derivative of f-1(x).
What is 1/(f'(f-1(x))?
This theorem states that every function that is continuous on an interval [a,b] has an absolute maximum and an absolute minimum somewhere on that interval.
What is the extreme value theorem?
These are Mr. Lester's cats names.
Who are Kenai, Mabel, and Luna?
This is the name for the limit technique I would employ if my limit is of indeterminate form but has an irrational expression in the numerator or denominator.
What is rationalization / multiplying by the conjugate on top and bottom?
This is the derivative of sin(3x5).
What is 15x4cos(3x5)?
This is the name of a limit technique in which I use denominators to convert out of an indeterminate form.
What is L'Hopital's rule?
What are critical numbers of f?
These two men are credited with inventing calculus. You will need both names.
Who are Newton and Liebniz?
This is the limit technique I would employ if x were approaching infinity for an expression whose numerator and denominator were both polynomials.
What is [i would look at the degrees and do some BOBO BOTNO EATSDC type stuff]?
This is the derivative of tan(x)/sqrt(x).
What is [yeah i'll just write it on the board]?
What are:
1. Write down a formula involving all parts.
2. Take the implicit derivative w.r.t. time (t).
3. Plug in everything I know.
4. Solve for what I don't know.
If f is concave down, this is true about f'.
What is f' is decreasing?
What is "biblical?"
This theorem states that if on an interval [a,b] containing c, that if h(x) < f(x) < g(x), and as x --> c, both h(x) --> L and g(x) --> L, that f(x) --> L must be true as well.
What is the squeeze theorem? [kick out anyone who said sandwich theorem]
This is the derivative of 2xcos(x2).
What is 2xln(2)cos(x2) + 2x(-sin(x2)(2x))?
This is how I can tell if a particle is slowing down.
If f' is increasing, this must be true about f.
What is f is concave up?
This is the last name of the man who actually proved L'Hopital's rule, although it was published in L'Hopital's book.
Who is Bernoulli?
This theorem states that if a function f(x) is cont. on [a,b], and f(a) > k > f(b) or f(a) < k < f(b), that there must exist an x-value c, a < c < b, such that f(c) = k.
What is the intermediate value theorem?
This is dy/dx if y3sin(x) + sec(y) = 13.
Find a linear approximation for the cube root of 29 using a tangent line constructed at x = 27. Answer must be given as a fraction.
What is 83/27?
State the Mean Value Theorem and its conditions verbatim (or close enough).
What is [i will judge]
This is how many multiple choice questions in total are on Monday's exam.
What is 27?