# Study sets matching "calculus 1"

Study sets

Diagrams

Classes

Users

End behavior

Exponential Decay

Exponential Growth

Limit

The appearance of a graph as it is followed farther and farthe…

A model for decay of a quantity for which the rate of decay is…

This model is used for such phenomena as inflation or populati…

The value that a function or expression approaches as the doma…

End behavior

The appearance of a graph as it is followed farther and farthe…

Exponential Decay

A model for decay of a quantity for which the rate of decay is…

Foundation 1: I can state 2 things that…

Foundation 2: I can state 2 things that…

Foundation 3

D1:

1.) The instantaneous rate of change and 2.) the slope of the…

1.) the net change; 2.) the area between a curve and the x-axis

I can estimate derivatives numerically

I can state what limits informally mean

Foundation 1: I can state 2 things that…

1.) The instantaneous rate of change and 2.) the slope of the…

Foundation 2: I can state 2 things that…

1.) the net change; 2.) the area between a curve and the x-axis

Real Number

Rational Number

Irrational Number

Integer

All rational and irrational numbers

Any number that can be expressed as a ratio of two integers

A number that cannot be expressed as a terminating or repeatin…

All whole numbers (both positive and negative) and zero.

Real Number

All rational and irrational numbers

Rational Number

Any number that can be expressed as a ratio of two integers

e

even or odd function

Intermediate Value Theorem

derivative of sin(x)

- e is a number... - inverse of e^x is ln(x)... - domain e^x : (-∞,∞…

f(-x) = - f(x) then it is odd... f(-x) = f(x) then it is even

the intermediate value theorem states: ... a continuous function…

cos(x)

e

- e is a number... - inverse of e^x is ln(x)... - domain e^x : (-∞,∞…

even or odd function

f(-x) = - f(x) then it is odd... f(-x) = f(x) then it is even

average velocity

limit

completing the square algebraic method

conjugate algebraic method

change in position over change in time

(IF) | f(x) - L | becomes arbitrarily small when x is any numb…

average velocity

change in position over change in time

limit

(IF) | f(x) - L | becomes arbitrarily small when x is any numb…

The (Limit) Definition of the Derivativ…

Mean Value Theorem

The Definition of Continuity at x=a

First Fundamental Theorem of Calculus

Suppose y=f(x) is continuous over a closed interval [a,b] and…

The (Limit) Definition of the Derivativ…

Mean Value Theorem

Suppose y=f(x) is continuous over a closed interval [a,b] and…

What would this graph look like?... y = x…

What are the two ways to check for x-in…

What are the two ways to check for y-in…

What are two ways to solve systems of e…

It would look like a parabola, shifted up one unit vertically.

1) Look at the graph for lines touching the x-axis... 2) Set y =…

1) Look at the graph for lines touching the y-axis... 2) set x =…

1) Substitution... 2) Elimination

What would this graph look like?... y = x…

It would look like a parabola, shifted up one unit vertically.

What are the two ways to check for x-in…

1) Look at the graph for lines touching the x-axis... 2) Set y =…

domain

range

y2-y1 / x2-x1

y-y1 = m(x-x1)

all of the x, or input, values of a function

all of the y, or output, values of a function

equation for slope of a line

equation for point-slope form

domain

all of the x, or input, values of a function

range

all of the y, or output, values of a function

Function

Domain

x²x³

x²/x³

Assigns to each number in its domain another number... Takes 1 i…

Consists of all numbers for which the rule makes sense. All nu…

x²⁺³

x²⁻³

Function

Assigns to each number in its domain another number... Takes 1 i…

Domain

Consists of all numbers for which the rule makes sense. All nu…

S

∈

⊆

U

set- collection of objects.... {a,b,c,d,e,f}... {all real numbers (R…

element of a set... a∈S meaning a is an element of the set (S) {a…

Subset meaning every object in one set is in another larger se…

union

S

set- collection of objects.... {a,b,c,d,e,f}... {all real numbers (R…

∈

element of a set... a∈S meaning a is an element of the set (S) {a…

f is continuous at x=c if...

Intermediate Value Theorem

Global Definition of a Derivative

Alternative Definition of a Derivative

If f is continuous on [a,b] and k is a number between f(a) and…

f '(x) is the limit of the following difference quotient as x…

f is continuous at x=c if...

Intermediate Value Theorem

If f is continuous on [a,b] and k is a number between f(a) and…