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UMD / Math / MATH 120 / What are the identities of factoring?

What are the identities of factoring?

What are the identities of factoring?

Description

School: University of Maryland - College Park
Department: Math
Course: Elementary Calculus
Professor: Hilaf hasson
Term: Spring 2017
Tags: Calculus
Cost: 50
Name: Study Guide For 10/04 Exam
Description: This is a compilation of all the objectives that we have gone over in chapters 1 through 2 that are probably going to be on the midterm.
Uploaded: 10/01/2017
28 Pages 73 Views 1 Unlocks
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CALCULUS

CH. 1 + CH. 2

NOTES

(STUDY GUIDE)

CH. 0.3 THE ALGEBRA OF FUNCTIONS

Operation on Functions → Like f(x) + g(x), f(x) - g(x), , f(x)g(x)

  • Basic properties of fractions
    1. Multiplication a・= and =
    2. Simplifying common factors =
    3. Division  = =
    4. Addition =
  • Adding Rational Functions
  • Ex.         g(x) =         h(x) = We also discuss several other topics like What does product configuration mean?

            g(x) + h(x) = + , x ≠ 0, 1Don't forget about the age old question of What is the hill equation?

    1. Find common denominator

    () + ()

    1. Multiply

    = +

    1. Combine

    = We also discuss several other topics like What do you think is the primary factor for soil production?

    1. Simplify

    =

    Composition of Functions (aka f(g(x)))

    Way of combining 2 functions f(x) and g(x), substituting variable x with g(x) in f(x)

  • Evaluating a Function
  • Ex. If f(x) = x3, find , where h ≠ 0

    1. Substitute

    f(x+h) = (x+h)3 = x3 + 3x2h + 3xh2 + h3

    1. Simplify

    f(x+h) - f(x) = (x3 + 3x2h + 3xh2 + h3) - x3 = 3x2h + 3xh2 + h3If you want to learn more check out n2cl4

    1. Factor H in Numerator

    We also discuss several other topics like presbyiatrics

    CH. 0.4 ZEROS OF FUNCTIONS - QUADRATIC FORMULA + FACTORING

            Quadratic Formula

  • Finding zeros of Functions
  • Ex. f(x) = 4x2 - 4x + 1

             = 4x2 - 4x + 1 = 0

    1. Quadratic Formula!

  • Finding Intersections of Graphs
  • Ex. Finding the points of intersection of graphs : y = x2 + 1 and y = 4x

    1. Equate two expressions for y (because coordinates must satisfy both eq.)

                    X2 + 1 = 4xDon't forget about the age old question of The communications technology is consist of?

            

    1. Quadratic Formula!

    1. Substitute x-values in equations to get y-values

    Factoring

  • Identities for factoring
    1. Difference of squares                 A2 - B2 = (A-B) (A+B)
    2. Perfect Square                A2 + 2AB + B2 = (A+B)2 or A2 - 2AB + B2 = (A-B)2
    3. Difference of Cubes                A3 - B3 = (A-B) (A2 - AB + B2)
    4. Sums of cubes                A3 + B3 = (A+B) (A2 - AB + B2)

    CH. 0.5 Exponents + POwer Functions

    Law of Exponents

    1. brbs = br+s Product Rule
    2. b-r =  Changing signs of exponents
    3.  Quotient Rule
    4. (br)s = brs                 Power of a power
    5. (ab)r = arbr                Power of a product
    6.                 Power of a Quotient

    Simple Compound Interest :

    Compound Interest w/ Multiple Interest Periods :

    WHERE P = principal amount (original amount deposited)

               r = interest rate per annum

               m = number of interest periods per year

               t = number of years

                i = compound interest rate per interest period

    1.1 The Slope of a Straight Line

            Slope-Intercept Equation        y = mx + b

            Point-Slope Form                y - y, m(x-x,)

    Parallel lines ➝ same slope

    Perpendicular Lines ➝ opposite reciprocal

    Be able to find:

  • Slope of line through two points
  • Equation of line given a point and a slope
  • Equation of line through 2 points
  • Equation of line parallel to a given line
  • 1.3 The Derivation and Limits

    Derivative of Linear Function : If mx + b = f(x), then f1(x) = m

    Constant Rule                f(x) = b ➝ f1(x) = 0

    Power Rule                f(x) = xr ➝ f1(x) = rxr-1

     

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