calc 2 midterm content Flashcards
What’s the distance formula?
What formula is this for?
What’s volume of a cone?
What volume is this:
Two ways for function to not be continuous? draw the options or map visually
(ig)corner/cusp, vertical tangents
If f has a local min or max at c, what does that indicate? Does that indicate any min/max? So what?
If what?: C must be a critical number of f, doesn’t indicate min or max. So must use a test to find if c is min or max
What does critical point mean?
(ig)f’(c) = 0 or undefined
What does continuous indicate for f(c)?
f(c) exists in the domain of f
How to find domain?
(ig)Plug denom = o and any points will have parenthesis like (-ifinity, 1) U (1,infinity) ;
U is “and”
How to find critical points from a function?
(ig) find the derivative, then equal numerator equal to 0, must factor out like x(x-2) for when the derivative to equal zero. Also check when derivative doesn’t exist by having denom(factor out) = 0, so the derivative doesn’t exist.
In terms of concavity test, how to know if concaves up or down?
(ig)
What’s an inflection point?
(ig)
What’s antiderivative of sin, cos
(ig) anti cos = sin + c
anti sin =-cos +c
What’s antiderivative of sec^2(x)
(ig) tan(x) + c
What’s antiderivative of sec(x) tan(x)
(ig) sec(x) + c
What’s antiderivative of csc^2(x)
(ig) - cot(x) + c
What is the limit of Riemann sum, also what does it mean, also explain how to find the components of it?
Define the picture and statement? This thing becomes an exact representation of the area under the curve from a to b.
the one with the limit is it, change of x and xi is shown to
What is xi and define/explain it? Also what is the i used to calculate it. Don’t give the equation for it.
(ig) i is an index that identifies each subinterval in the partition of the interval. xi represents the sample point within each subinterval.
How to calculate xi
(ig)
How to calculate trapezoid area?
What does this calculate:
When do you use chain rule on the integral?
(ig) When it’s for for the first fundamental thereom:
