# dx & lim

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 Author: jojobean0203 ID: 203202 Filename: dx & lim Updated: 2013-05-27 19:28:57 Tags: dx Folders: Description: dx Show Answers:

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• m tangent =
1. find equation of secant line
2. 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
3. define derivative of a function
4. how is continuity of a function related to limit?
• f(x) is continuous at x = a when:
5. squeeze theorem:

range of sin: [-1,1]

lim as x goes to 0: 0 < 0 < 0
6. squeeze theorem:

7. derive formulas for:
circle
- circumference
- area
sector
- length
- area
sphere
- volume
- area
• circle

• sector

• sphere

8. 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

9.  = 0
• r is a positive rational number
• if r > 0 & x > 0, x^r will go to infinity, & 1/x^r will approach 0
10. principal values of inverse trig fxns

11. prove:

substitute

factor out c

= c f'(x)
12. prove

13. 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
14. 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
15. 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
16. if f(x) <g(x) in a neighborhood around x = a; what must be true about their limits?
17. does not exist
18. 1
19. 0
20. 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
21. 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
22. the line y = L is a horizontal asymptote of the curve y = f(x) if:
• either:

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