limits, continuity, and differentiability
the two types of discontinuity
what is removable and nonremovable
the derivative of cos(x)
what is -sin(x)
set up AROC
what is f(b)-f(a)/b-a
what theorem sets the average rate of change equal to instantaneous
what is mean value theorem
the three types of sums
what is a right riemann sum, left riemann sum, and a trapezoidal sum
the lim x->0 of tan(x)/x
what is 1
the derivative of arctan(x)
what is 1/1+x2
how speed is represented
what is the absolute value of velocity
write out what the extreme value states (what has to be true and what exists because of this)
what is "if a function f is continuous on [a,b] then an absolute maximum and minimum must exist on the interval"
is a right riemann sum an underestimate or an overestimate
what is an overestimate
the three types of nonremovable discontinuity
what is jump, infinite, and oscillating
the derivative of cos2(5x2)
what is -20xcos(5x2)sin(5x2)
what the first, second, and third derivatives of position represent
what are velocity, acceleration, and jerk
find the solution to the equation y=x2 on the interval [0,2] that satisfies the mean value theorem
what is x=1
evaluate the indefinite integral (4x6 - 2x3 + 7x - 4)dx
what is 4/7x7 - 1/2x4 + 7/2x2 - 4x + c
what must be true in order for a function to be continuous at a point (3)
what is "it must be defined at that point, its limit must exist at that point, and the value of the function at that point must be equal to the value of the limit"
write out the product rule and quotient rule
what is uv=u(x)v'(x)+v(x)u'(x) and lo di hi - hi di lo all over lo squared
if s is measured in inches and A is measured in square inches, what units are appropriate for dA/ds
what is in2/in
let f be a continuous function on the closed interval [1,5] where f(1)=1 and f(5)=-3. fill in the blanks for what can be guaranteed by the intermediate value theorem
f(c)= ___ for a least one c between ___ and ___
what is f(c)= (value between -3 and 1) for at least one c between (1) and (5)
determine f(x) given that f'(x)=12x2-4x and f(-3)=17
what is f(x)= 4x3 - 2x2 + 143
the four types of nondifferentiable functions (what is formed)
what are cusps, corners, vertical tangents, and any discontinuities
write out the h definition and alternate definition
what is lim h->0 of f(x+h)-f(x)/h and lim x->a of f(x)-f(a)/x-a
find the rate of change of the area A of a circle with respect to its radius r
what is dA/dr=2ℼr
find the absolute extrema of f(x)=4/3x3-2x2 on the interval [-3,3]
what is (3,18) and (-3,-54)
determine the area below f(x)=-x2+2x+3 and above the x-axis
what is 32/3