AP Calculus Vocabulary Flashcards Preview

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Flashcards in AP Calculus Vocabulary Deck (61)
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1

discontinuity or jump

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

2

limit

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

3

infinity

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

4

removable

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

5

zero

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

6

one-sided limit

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)

7

quotient rule

d/dx(u/v)=vu'-uv'/v^2

8

derivative of e^x

e^x

9

chain rule

d/dx(f(g(x)))=f'(g(x))*g'(x)

10

derivative of sin(x)

cos(x)

11

power rule

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

12

derivative of ln(x)

1/x

13

derivative

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

14

product rule

d/dx(uv)=uv'+vu'

15

derivative of log(a)x

1/x(ln(a))

16

derivative of cos(x)

-sin(x)

17

velocity

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

18

slope of a tangent line

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

19

equation of a tangent line

y-y1=m(x-x1)

20

position

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

21

acceleration

the second derivative of position

22

jerk

the third derivative of position

23

implicit differentiation

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

24

optimization

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

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