dx & lim

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1. • • m tangent = 2. find equation of secant line 3. 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
4. define derivative of a function 5. how is continuity of a function related to limit?
• f(x) is continuous at x = a when:
• 6. squeeze theorem: range of sin: [-1,1]  lim as x goes to 0: 0 < 0 < 0
7. squeeze theorem: 8. derive formulas for:
circle
- circumference
- area
sector
- length
- area
sphere
- volume
- area
• circle
• • • sector
• • • sphere
•  9. 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
10.  = 0
• r is a positive rational number
• if r > 0 & x > 0, x^r will go to infinity, & 1/x^r will approach 0
11. principal values of inverse trig fxns   12. prove:    substitute factor out c = c f'(x)
13. prove    14. difference between essential, non-essential, & removal discontinuity
essential: can't be patched; graph has a break:(2,3) & (2, 5) breaks at x = 2

• non-essential: removable discontinuity, can be patched,
• • if these are = (both 9), can patch by defining f(3) = 9
15. what must be true to repair a discontinuity?
• the 2 one-sided 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
16. 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
17. if f(x) <g(x) in a neighborhood around x = a; what must be true about their limits? 18. does not exist
19. 1
20. 0
21. 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
22. 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
23. the line y = L is a horizontal asymptote of the curve y = f(x) if:
• either:
• 24.  Author: jojobean0203 ID: 203202 Card Set: dx & lim Updated: 2013-05-27 23:28:57 Tags: dx Folders: Description: dx Show Answers: