Calc1 Flashcards Preview

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Flashcards in Calc1 Deck (86):
1

sequence

1

2

limit of sequence

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3

sequence convergence

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defn, divergent, two types

4

monotonic

4

5

bounded

5

6

convergent sequence properties

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10 of em

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limits of functions

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defn, below, above, limit

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properties of limits of functions

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5 of em

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limit of functions as x→±∞

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10

special limits

10
4 general ones, 4 for a > 1, 4 for 0

11

f continuous at a

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12

properties of continuous functions

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3 continuous everywhere, 3 continuous where they're defined, 4 properties, chain rule

13

extreme value theorem

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14

Bolzano's theorem

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f(c)=0

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intermediate value theorem

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16

Brouwer's fixed-point theorem

16

17

derivative

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defn, tangent line, continuity

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derivative properties

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6 of em

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common derivatives

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22 of em: k, x^k, e^x, a^x, logx, log_ax, log_a|x|, sin, cos, tan, cot, sec, csc, asin, acos, atan, csc^-1, sec^-1, cot^-1, sinh, cosh, tanh

20

implicit differentiation

20

21

higher order derivatives

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properties of the first derivative

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f'(x) ,= 0

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critical point of f

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properties of the second derivative

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25

inflection point

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26

local minimum/maximum

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27

nth derivative test

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28

absolute minimum/maximum

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extremum

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Rolle's theorem

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f'(c)=0

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mean-value theorem for derivatives

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32

related rates

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33

indefinite integral

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34

common integrals

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k, x^k, 1/x, 1/(x-a), 1/(x^2+a^2), x/(x^2+a^2), e^(ax), a^x, sin(ax), cos(ax), sec^2(x), csc^2(x), secx tanx, cscx cotx, 1/sqrt(1-x^2), 1/(1+x^2)

35

integration by substitution

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ex. x^2(x^3+4)^5

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integration by parts

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ex. x*logx

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trig substitutions

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3 substitutions

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method of partial fractions

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ex. 1/(x^4-x^2)

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definite integral

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Riemann sum

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properties of definite integral

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6 of em

42

fundamental theorem of calculus

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2 parts

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mean-value theorem for integrals

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44

area between two curves

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45

cartesian coordinates

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46

polar coordinates

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conversions of cartesian to polar

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48

derivative of polar coordinates

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area enclosed by polar equation

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arc length for polar coordinates

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51

solid of revolution

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volume of the solid of revolution

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53

formula for arc length

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54

formula for surface area, 1D

54
function rotated about x or y axis

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calculating the center of mass

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56

exponential e

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57

natural exponential / logarithm functions

57
defn, defn, property

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indeterminate form

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L'Hôpital's rule

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60

improper integrals

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61

improper integral kinds

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62

infinite series

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partial sums

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64

convergence of infinite series

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defn

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geometric series

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harmonic series

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convergence tests for infinite series

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3 of em

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p-series

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69

comparison test / limit comparison test

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ratio test

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root test

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integral test

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alternating series

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alternating series test

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absolute convergence

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converges absolutely, converges conditionally, thrm

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power series

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radius of convergence of a power series

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function defined by a power series

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properties of functions defined by power sereis

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3 of em

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Taylor series

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common Taylor series

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1/(1-x), 1/(1+x), log(1+x), e^x, sinx, cosx

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Taylor polynomial

82
defn, error

83

series in powers of (x-a)

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series, Taylor coefficients, error

84

parametric equations, derivatve

84

85

parametric equations, area under the curve

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86

parametric equations, arc length

86