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