AP Calculus Theorems and Concepts "Limits" (Chapter 1)
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| Definition: The Intermediate Value Theorem (IVT) | show 🗑
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| Concept: Continuity of a function | show 🗑
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| Concept: Fundamental Theorem of Algebra | show 🗑
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| show | When a function "f" is defined at every point on an interval except for one value, say "c". At this location the Lim as x approaches from both the right and left equals some specific value such as y=12 but f(c) ≠ 12. "Concept of hole in graph"
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| Definition: Infinite Discontinuity | show 🗑
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| Definition: Jump Discontinuity | show 🗑
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| Definition: Average Rate of Change | show 🗑
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| show | Let "f" be a function defined at every point "c" on the open interval (a,b) except possible at "c" itself,
If there exists a real number L such that the limit as x approaches c from both the right and left,
then we say the limit exists.
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| show | 1) Jump, Step, or Gaps
2) Oscillating Functions
3) Unbounded Behavior
Be able to supply examples of each with appropriate limits when asked.
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| show | 1) Crude Method: Table of values or Graph
2) Direct Substitution
3) Factoring Expression
4) Using common denominators
5) Conjugates
6) Trig Theorems
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| show | A function "f"is said to be this if for every c that is an element of
( a , b ) there exists a limit as x approaches c from both the right and left to which equals f (c).
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| show | (A–B)(A^2+AB+B^2)
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| show | (A+B)(A^2–AB+B^2)
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| show | sin (x + y) = sin(x)cos(y) + sin(y)cos(x)
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| show | sin (x – y) = sin(x)cos(y) – sin(y)cos(x)
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| Sum formula for cosine | show 🗑
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| show | cos (h – k) = cos(h)cos(k) + sin(h)sin(k)
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| Double angle formula for sine | show 🗑
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| Double angle formula for cosine | show 🗑
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| show | sin^2 (g) + cos^2 (g) = 1
1 + cot^2(j) = csc^2 (j)
tan^2 (m) + 1 = sec^2 (m)
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| show | lim t–>0 sin (t) /t = 1
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| show | lim r–>0 (1–cos (r) )/ r = 0
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