Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

AP Calculus > AP Calculus Vocabulary > Flashcards

AP Calculus Vocabulary Flashcards

1
Q

discontinuity or jump

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

limit

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

removable

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
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)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

quotient rule

A

d/dx(u/v)=vu’-uv’/v^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

derivative of e^x

A

e^x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

chain rule

A

d/dx(f(g(x)))=f’(g(x))*g’(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

derivative of sin(x)

A

cos(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

power rule

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

derivative of ln(x)

A

1/x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

derivative

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

product rule

A

d/dx(uv)=uv’+vu’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

derivative of log(a)x

A

1/x(ln(a))

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

derivative of cos(x)

A

-sin(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

velocity

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

slope of a tangent line

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

equation of a tangent line

A

y-y1=m(x-x1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

position

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

acceleration

A

the second derivative of position

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

jerk

A

the third derivative of position

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

implicit differentiation

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

optimization

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

grpahical analysis

A

the use of the original function and it’s first and second derivatives to determine the graphical behaviors of a given function

26
Q

maximum

A

what occurs when the first derivative is equal to zero or is undefined and also changes from positive to negative

27
Q

minimum

A

what occurs when the first derivative is equal to zero or is undefined and also changes from negative to positive

28
Q

critical point

A

where the first derivative is either equal to zero or undefined

29
Q

concave up

A

what occurs on a graph of the original function when the second derivative is positive

30
Q

concave down

A

what occurs on a graph of the original function when the second derivative is negative

31
Q

point of inflection

A

f’(c)=f(b)-f(a)/b-a on [b,a] if the function is continuous and differentiable

32
Q

mean value theorem

A

where the second derivative is equal to zero or is undefined

33
Q

anti-derivative

A

what one takes the derivative of to arrive at a given function

34
Q

initial value problem

A

solving for c when given a derivative and a point that exists on the original graph

35
Q

constant

A

what must be added on to the end of an anti-derivative in order to consider all cases of that anti-derivative

36
Q

u-substitution

A

what can be used to integrate something that appears to be a chain rule of some sort

37
Q

slope field

A

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
Q

LRAM

A

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
Q

RRAM

A

estimating area using rectangles and using the right hand side of the subinterval to determine the height of the rectangle

40
Q

MRAM

A

estimating area using rectangles and using the middle of the suinterval to determine the height of the rectangle

41
Q

reimann sum

A

using rectangles that are not measured in equal subintervals to estimate the area between a curve and the x-axis

42
Q

pi*r^2

A

area of a circle

43
Q

1/2bh

A

area of a triangle

44
Q

b^2

A

area of a square

45
Q

integral

A

? function dx

46
Q

limits

A

from where to where (function values) an integral is evaluated

47
Q

dx

A

what is included on the end of an integral to let one know that the integral is taken with respect to x

48
Q

fundamental theorem of calculus part 1

A

d/dx?a-x f’(x) dt= f(x)

49
Q

fundamental theorem of calculus part 2

A

?a-b f(x) dx = F(a)-F(b) if f(x) is continuous on [a,b]

50
Q

definite integral

A

the sign that is used to indicate finding the area that exists between the curve and the x-axis

51
Q

area between two curves

A

found by ?a-b top-bottom dx

52
Q

accumulation

A

when areas between the curve and the x-axis represent a gathering of something (like distance traveled)

53
Q

net change

A

?a-b(function adding something) dt - ?a-b (function subtracting something) dt

54
Q

average rate of change when given a rate

A

1/a-b ?a-b f(x) dx

55
Q

L’Hopitals rule

A

procedure by which one can take the limit of a function that was previously thought to be indeterminant

56
Q

cross sections

A

what we use to find the volume generated by using shapes that span a base with two functions

57
Q

disk method

A

the process of revolving the area of one function around the x-axis

58
Q

washer method

A

the process of revolving the area of two functions around the x-axis

59
Q

revolving around x-axis

A

?a-b pi(furthest^2-closest^2) dx

60
Q

revolving around y-axis

A

?a-b pi(furthest^2-closest^2) dy

61
Q

revolving around other axes

A

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)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions