Calculus 1

Vertical and horizontal shifts and stretch Reflections

+ shifts up - shifts down - reflects about x-axis + reflects about y-axis

Conjugates of a function

-

One sided Limits

- = approaches from the right.. + approaches to the left. Learn how to do it. * know how to determine if its DNE or UDF

Velocity

- The law of gravitation on the earth says that distance traveled by an object that is freefalling. s(t) = 1/2 gt^2 s = measurement by Meters/feet T = measurment by seconds G = measurement of gravitation

Composition

- given F and G. The composite function F*G is defined as F composed by G = F(G(x)) where F is primary and G is secondary.

Polynomial Theorem

Any polynomial function is continuous everywhere on ( - infinity, infinity)

Rational Theorem

Any rational functions is continuous wherever it is defined (in its domain)

Root theorem

Any root function is continuous is continuous in its domain

Derivatives

F'(x) = lim f(x+h) - f(x) as h goes to 0.

Piecewise functions

Function expressed by two or more different formulas over different pieces of intervals

Infinite Limits

Know how to do this - Let f(x) be a function defined on an open interval containing a real number C, but f(x) is not defined at C then the limit of f(x)equals to infinity as x approaches C. can be negative or positive infinity

Squeeze Theorem

Know how to use Squeeze Theorem

Limit of a Function

Look at example problems solve or simplify then insert whatever x is Let F(x) be a function defined on an open interval that continues a number C but possibly not defined at C. then the limit as x approaches C is written as Lim f(x) = L as x approaches c

Trigonometric Functions

Sine X Cos X Tan X Sec X CSC X CoTan X

Greatest integer theorem

The greatest integer function is continuous everywhere except all integer numbers.

Continuity

Understand what it is and how it works. why its not continuous at certain spots

Logarithmic Function

and/or A^y = X

Trigonometric theorem

any trigonometric function is continuous in its domain

Derivatives of trigonometric functions

d/dx (sin x) = cos x d/dx (cos x) = - sin x d/dx (tan x) = sec^2 X d/dx (cotan x) = - csc^2 x d/dx (sec x) = (sec x)(tan x) d/dx (csc x) = (- csc x)(cotan x )

Writing notation for a derivative

f'(x) = y' = dy/dx = d/dx f(x) Prime Notations Leibrig notation

Vertical line

vertical line x = c is called a vertical asymptote of y = f(x) is undefined at x = c and lim f(x) = infinity / - infinity as x approaches c

higher order of sin cos etc...

y = sin x 1. (sin x)' = cos x 2. (sin (x))'' (cos x)' = - sin x 3. (sin x)''' = (-sin x)' = - cos x 4. (sin x)'''' = (-cos x)' = sin x. --> same as above with the y = sin x. find 27th derivative: - 4th is the same function 27/ 4 = 24 r 3 = sin x^3 with the 3rd form = - cos x