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Copyright & License Copyright c 2007 Jason Underdown Some rights reserved. Calculus I 
Formula quadratic formula Calculus I 

Definition absolute value Calculus I 
Theorem properties of absolute values Calculus I 

Definition equation of a line in various forms Calculus I 
Definition equation of a circle Calculus I 

Definition sin, cos, tan Calculus I 
Definition sec, csc, tan, cot Calculus I 

Definition midpoint formula Calculus I 
Definition function Calculus I 

The solutions or roots of the quadratic equation ax^{2} + b x + c = 0 are given by 
These flashcards and the accompanying
source code are licensed under a Creative Commons Attribution–NonCommercial–ShareAlike 2.5 License. For more information, see creativecommons.org. You can contact the author at: jasonu at physics utah edu File last updated on Sunday 8^{th} July, 2007, at 17:15 

The equation of a circle centered at (h, k) with
radius r is: (x − h)^{2} + (y − k)^{2} = r^{2} 


A function is a mapping that associates with each object x in one set, which we call the domain, a single value f (x) from a second set which we call the range. 
If P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) are two points, then
the midpoint of the line segment that joins these two points is given by: 

Definition even and odd functions Calculus I 
Definition limit Calculus I 

Definition one–sided limit Calculus I 
Theorem limit exists iff both the right–handed and left–handed limits exist and are equal Calculus I 

Theorem main limit theorem (part 1) Calculus I 
Theorem main limit theorem (part 2) Calculus I 

Theorem squeeze theorem Calculus I 
Theorem two special trigonometric limits Calculus I 

Definition pointwise continuity Calculus I 
Theorem composition limit theorem Calculus I 

If a function f (x) is defined on an open interval
containing c, except possibly at c, then the limit of f (x) as x approaches c equals L is denoted The above equality holds if and only if for any there exists such that 
even f(−x) = f (x) for all x e.g. x^{2}, cos (x) odd f(−x) = −f (x) for all x e.g. x, sin (x) 

right–handed limit iff for any there exists a such that 

Let f, g be functions that have limits at c, and
let n be a positive integer. 7. if 8. 9. provided that when n is even. 
Let k be a constant, and f, g be functions that
have limits at c. 

Suppose f, g and h are functions which satisfy
the inequality for all x near c, (except possibly at c). Then


If and f is continuous at L, then 
Let f be defined on an open interval containing
c, then we say that f is pointwise continuous at c if


Definition continuity on an interval Calculus I 
Definition derivative Calculus I 

Definition equivalent form for the derivative Calculus I 
Theorem differentiability and continuity Calculus I 

Theorem constant and power rules Calculus I 
Theorem differentiation rules Calculus I 

Theorem derivatives of trig functions Calculus I 
Theorem chain rule Calculus I 

Theorem generalized power rule Calculus I 
Definition notation for higherorder derivatives Calculus I 

The derivative of a function f is another
function f' (read “f prime”) whose value at x is provided the limit exists and is not ∞ or −∞. 
function f is said to be continuous on an open inteval iff f is continuous at every point of the open interval. A function f is said to be continuous on a closed interval [a, b] iff 1. f is continuous on (a, b) and 2. and 3. 

If the function f is differentiable at c, then f
is continuous at c. 

Let f and g be functions of x and k a constant. 1. scalar product rule (k f)' = k f' 2. sum rule (f + g)' = f' + g' 3. difference rule (f − g)' = f' − g' 4. product rule (f g)' = f' g + f g' 5. quotient rule 

Let u = g (x) and y = f (u). If g is differentiable
at x, and f is differentiable at u = g (x), then the composite function is differentiable at x and
In Leibniz notation 


If f is a differentiable function and n is an
integer, then the power of the function
is differentiable and 

Theorem extreme value theorem Calculus I 
Theorem intermediate value theorem Calculus I 

Definition critical point stationary point singular point Calculus I 
Definition increasing decreasing monotonic Calculus I 

Theorem monotonicity theorem Calculus I 
Definition concave up concave down Calculus I 

Theorem concavity theorem Calculus I 
Definition inflection point Calculus I 

definition local maximum local minimum local extremum Calculus I 
Theorem first derivative test Calculus I 

If the function f is continuous on the closed
interval [a, b] and v is any value between the minimum and maximum of f on [a, b], then f takes on the value v. 
If the function f is continuous on the closed
interval [a, b], then f has a maximum value and a minimum value on the interval [a, b]. 

A function f defined on the interval I is • increasing on I , for every • decreasing on I , for every The function f is said to be monotonic on I if f is either increasing or decreasing on I. 
If f is a function defined on an open interval
containing the point c, we call c a critical point of f iff either • f' (c) = 0 or • f' (c) does not exist Furthermore when f' (c) = 0 we call c a stationary point of f, and when f' (c) does not exist we call c a singular point of f. 

Suppose f is differentiable on an open interval
I, then if f' is increasing on I we say that f is concave up on I. If f' is decreasing on I we say that f is concave down on I. 
Suppose f is differentiable on an open interval
I, then • f' (x) > 0 for each is increasing on I • f' (x) < 0 for each is decreasing on I 

Let f be continuous at c, then the ordered pair
(c, f (c)) is called an inflection point of f if f is concave up on one side of c and concave down on the other side of c. 
Let f be twice differentiable on the open
interval I. • f'' (x) > 0 for each is concave up on I • f'' (x) < 0 for each is concave down on I 

Let f be differentiable on an open interval (a,
b) that contains c. 1. and is a local maximum of f. 2. and is a local minimum of f. 3. If f' (x) has the same sign on both sides of c, then f (c) is not a local extremum. 
Let the function f be defined on an interval I
containing c. We say f has a local maximum at c iff there exists an interval (a, b) containing c such that f (x)≤ f (c) for all x ∈ (a, b). We say f has a local minimum at c iff there exists an interval (a, b) containing c such that f (x) ≥f (c) for all x ∈ (a, b). A local extremum is either a local maximum or a local minimum. 

Theorem second derivative test Calculus I 
Theorem mean value theorem Calculus 

If f is continuous on a closed interval [a, b]
and differentiable on its interior (a, b), then there is at least one point c in (a, b) such that or equivalently f (b) − f (a) = f' (c)(b − a) 
Let f be twice differentiable on an open interval
containing c, and suppose f' (c) = 0. 1. If f'' (c) < 0, then f has a local maximum at c. 2. If f'' (c) > 0, then f has a local minimum at c. 3. If f'' (c) = 0, then the test fails. 