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AP Calculus > AP Calculus Vocabulary > Flashcards

AP Calculus Vocabulary Flashcards

(61 cards)

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1
Q

discontinuity or jump

A

the x-value at which a limit will not exist due to a sudden change in y-value

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2
Q

limit

A

a y-value that a function approaches as x-values get closer and closer to a specified number

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3
Q

infinity

A

what a limit approaches as it gets closer to an asymptote, or the behavior of a rational function as x approaches infinity and the power on top is larger than the power on the bottom

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4
Q

removable

A

type of discontinuity that is usually characterized by a hole in the graph

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5
Q

zero

A

the behavior of a rational function as x approaches infinity if the power on bottom is larger than the power on top

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6
Q

one-sided limit

A

a limit that only takes into account what y-value is being approached from one side of the function (susually denoted by a plus or minus)

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7
Q

quotient rule

A

d/dx(u/v)=vu’-uv’/v^2

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8
Q

derivative of e^x

A

e^x

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9
Q

chain rule

A

d/dx(f(g(x)))=f’(g(x))*g’(x)

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10
Q

derivative of sin(x)

A

cos(x)

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11
Q

power rule

A

d/dx(u^n)=nu^n-1

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12
Q

derivative of ln(x)

A

1/x

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13
Q

derivative

A

formal name for the instantaneous rate of change or slope of the tangent line

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14
Q

product rule

A

d/dx(uv)=uv’+vu’

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15
Q

derivative of log(a)x

A

1/x(ln(a))

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16
Q

derivative of cos(x)

A

-sin(x)

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17
Q

velocity

A

the first derivative of position or the anti-derivative of acceleration

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18
Q

slope of a tangent line

A

found by taking the derivative and plugging in a specified x-value

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19
Q

equation of a tangent line

A

y-y1=m(x-x1)

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20
Q

position

A

generally a function given that determines where something is at a given time or the anti-derivative of velocity

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21
Q

acceleration

A

the second derivative of position

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22
Q

jerk

A

the third derivative of position

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23
Q

implicit differentiation

A

taking the derivative of an equation that has x’s and y’s intermixed

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24
Q

optimization

A

process by which we use the derivative to maximize or minimize a given function

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25
grpahical analysis
the use of the original function and it's first and second derivatives to determine the graphical behaviors of a given function
26
maximum
what occurs when the first derivative is equal to zero or is undefined and also changes from positive to negative
27
minimum
what occurs when the first derivative is equal to zero or is undefined and also changes from negative to positive
28
critical point
where the first derivative is either equal to zero or undefined
29
concave up
what occurs on a graph of the original function when the second derivative is positive
30
concave down
what occurs on a graph of the original function when the second derivative is negative
31
point of inflection
f'(c)=f(b)-f(a)/b-a on [b,a] if the function is continuous and differentiable
32
mean value theorem
where the second derivative is equal to zero or is undefined
33
anti-derivative
what one takes the derivative of to arrive at a given function
34
initial value problem
solving for c when given a derivative and a point that exists on the original graph
35
constant
what must be added on to the end of an anti-derivative in order to consider all cases of that anti-derivative
36
u-substitution
what can be used to integrate something that appears to be a chain rule of some sort
37
slope field
what is used to get an idea of what the original function may look like based on the derivative and slopes at particular points
38
LRAM
estimating area between the curve and the x-axis using rectangles and using the left hand side of the subinterval to determine the height of the rectangle
39
RRAM
estimating area using rectangles and using the right hand side of the subinterval to determine the height of the rectangle
40
MRAM
estimating area using rectangles and using the middle of the suinterval to determine the height of the rectangle
41
reimann sum
using rectangles that are not measured in equal subintervals to estimate the area between a curve and the x-axis
42
pi*r^2
area of a circle
43
1/2*b*h
area of a triangle
44
b^2
area of a square
45
integral
? function dx
46
limits
from where to where (function values) an integral is evaluated
47
dx
what is included on the end of an integral to let one know that the integral is taken with respect to x
48
fundamental theorem of calculus part 1
d/dx?a-x f'(x) dt= f(x)
49
fundamental theorem of calculus part 2
?a-b f(x) dx = F(a)-F(b) if f(x) is continuous on [a,b]
50
definite integral
the sign that is used to indicate finding the area that exists between the curve and the x-axis
51
area between two curves
found by ?a-b top-bottom dx
52
accumulation
when areas between the curve and the x-axis represent a gathering of something (like distance traveled)
53
net change
?a-b(function adding something) dt - ?a-b (function subtracting something) dt
54
average rate of change when given a rate
1/a-b ?a-b f(x) dx
55
L'Hopitals rule
procedure by which one can take the limit of a function that was previously thought to be indeterminant
56
cross sections
what we use to find the volume generated by using shapes that span a base with two functions
57
disk method
the process of revolving the area of one function around the x-axis
58
washer method
the process of revolving the area of two functions around the x-axis
59
revolving around x-axis
?a-b pi(furthest^2-closest^2) dx
60
revolving around y-axis
?a-b pi(furthest^2-closest^2) dy
61
revolving around other axes
process by which we move an area to revlove around an axis by shifting them up, down, left, or right to find the voulme generated by revolving said areas

AP Calculus (1 decks)

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