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 m tangent =

find equation of secant line

acceleration
speed
velocity
 speed
  absolute value of velocity; does not have direction; magnitude component of velocity
  rate of change of position
  distance moved per unit of time
  s(t) = position fxn
 velocity
  contains both magnitude + direction
  s'(t) = velocity fxn
 acceleration
  rate of change of velocity
  s"(t) = acceleration nfxn

define derivative of a function

how is continuity of a function related to limit?
 f(x) is continuous at x = a when:

squeeze theorem:
range of sin: [1,1]
lim as x goes to 0: 0 < 0 < 0

squeeze theorem:

derive formulas for:
circle
 circumference
 area
sector
 length
 area
sphere
 volume
 area

intermed value therem
 function continuous over closed interval [a, b]
 if :
 for any value d between f(a) & f(b), excluding f(a) & f(b), there is a c between (a,b) such that f(c) = d

= 0
 r is a positive rational number
 if r > 0 & x > 0, x^r will go to infinity, & 1/x^r will approach 0

principal values of inverse trig fxns

prove:

prove

difference between essential, nonessential, & removal discontinuity
essential: can't be patched; graph has a break:(2,3) & (2, 5) breaks at x = 2
 nonessential: removable discontinuity, can be patched,

 if these are = (both 9), can patch by defining f(3) = 9

what must be true to repair a discontinuity?
 the 2 onesided limits must be the same: the limit of f(x) as x approaches c from the left and right must be equal
 then f(x) can be repaired by defining f(c) = L

methods for finding/evaluating limit of a fxn
 using table of values as x gets closer & closer to a
 graphically
 algebraically using limit laws
 using trig identities

if f(x) <g(x) in a neighborhood around x = a; what must be true about their limits?




what conditions must be met before taking the limit of a composite function?
 for 1 > 2:
 is in domain of f(x)
 f & g are continuous

interval continuity
 f(x) is continuous on an interval if it is continuous at q # in the interval
 if f is defined on only one side of an endpoint, continuous at the endpoint means continuous from the right or continuous from the left

the line y = L is a horizontal asymptote of the curve y = f(x) if:
 either:


