AP Calc

Limits

100

Lim xsinx

X->0

0

200

Lim x²-6x+8/x-4

X->4

2

300

Lim (1/x-1/2)/x-2

X->2

-1/4

400

Lim (1/x+5)-(1/5)/x

x->0

-1/5x+25

500

Lim cos(pi/2(x))

X->2

-1

Power Rule for Derivatives

100

D/dx x⁴

4x³

200

D/dx (x)

1

300

F(x)=1/x⁴

-4/x⁵

400

F(x)=-2a²+3a-6

-4a+3

500

F(x)=a⁴-4/a³

4a³+12/a³

Definitions

100

Functions whose graphs can be drawn without removing your pencil from the paper

Continuous functions

200

___ rate of change is the rate of change at any given instant.

Instantaneous

300

If any two functions ___ together at a particular point, then any function trapped between them will get ___ to that same point.

Squeeze theorem

400

A number that a function is approaching as the independent variable of the function approaches a given value.

Limit

500

___ tells us the slop of a function at any given point

Derivatives

IVT & Limits to Infinity

100

If f(x)=3-x², will f(x)=0 on the interval (-3,2)

According to the IVT, there is a value c such that f(c)=0 and -3<c<2

200

Lim (x²)

X->infinity

+infinity

300

If f(x)=1/x, will f(x)=-1 on the interval (1,4)

There is no guarantee that f(x)=-1, but f(x) might =-1

400

Lim 8x+2/2x+5

X->infinity

0

500

If f(x)=3x²-10x+2, will f(x)=1 on the interval (-2,3)

According to IVT, this is such value c such that f(c)=1 and -2<c<3

Average Rate of Change

100

F(x)=x²-2 (-1,3)

2

200

F(x)=2^x (2,4)

6

300

f(x)=tan(x)+4 (pi/4,3pi/4)

-1.27

400

F(x)=lnx 2<x<7

0.252

500

F(x)=cosx -1<x<0

0.46