Flashcards
Calculus Honors MidTerm Definitions
Cards in this deck (19)
- 1why is a sequence a simple function?A sequence is a simple function because there is a rule that assigns each and every element in the domain to only and only one element in the range.
- 2sequenceA sequence is a "simple" function because the domain is restricted to the set of natural numbers
- 3Limits of Sequences: Theorem 1 (constant)Limit of a constant = the constant
- 4Theorem 2 (positive exponent)Limit of pⁿ where n > 0, and p is positive = ∞
- 5Theorem 3 (denominator)Limit of 1/pⁿ and n > 0 = 0 (denominator dominates numerator)
- 6Theorem 4 (fractional exponent)Limit of pⁿ and -1 < p < 1 = 0
- 7Theorem 5Limit of a sum is the sum of the two limits
- 8Theorem 6Limit of a difference is the difference of the two limits
- 9Theorem 7Limit of a product is the product of the two limits
- 10Theorem 8Limit of a quotient is the quotient of the two limits
- 11Special Limitslim (x→0) of Sin x/ x =1
lim (x→0) of (1-cos x)/x =0
lim (x→0) (1 + 1/x)^x = e - 12Continuity ConditionsLim f(x) must exist at f(x) (be defined at x=a)
Lim (x→a⁻) f(x) = Lim (x→a⁺) f(x)
Lim (x→a) f(x) = f(a) - 13Rational Functions-discontinuous where denominator = 0
-removable discontinuities
-infinite discontinuities - 14Piecewise Functions-removable discontinuities
-jump discontinuities - 15Polynomial Functionscontinuous everywhere
- 16continuity at a point x = adefined at f(a)
- 17continuity on an intervalcontinuous everywhere
- 18limit definitionrepresents the slope of the line tangent to the function f(x) at the point (x, f(x)). The significance is the instantaneous rate of change in the value of the function at
(x, f(x))
- 19—represents the slope of the line secant to the function f(x) through (x, f(x)) and (x+h, f(x+h)). The significance is the average rate of change in the value of the function through (x, f(x)) and (x+h, f(x+h))
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- Calculus Honors Flashcards on Calculus Honors MidTerm Definitions, created by Emma Taff on 15/01/2019.
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