Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate…

Slides:



Advertisements
Similar presentations
4.5 Complex Numbers Objectives:
Advertisements

Section P3 Radicals and Rational Exponents
Multiply complex numbers
Zero Exponent? Product or quotient of powers with the same base? Simplify Negative Exponents.
5.6 Solving Quadratic Equations
Exponents, Polynomials, and Polynomial Functions.
Laws of Exponents. Day 1: Product and Quotient Rules EXP 1.1 I can use the Product and Quotient Rules to simplify algebraic expressions.
Damia D Bases and Exponents An exponent tells you how many times the base is multiplied by itself. x 4 = x ·x ·x ·x In this case, the larger number,
RATIONAL EXPONENTS Assignments Assignments Basic terminology
EXAMPLE 1 Evaluate numerical expressions a. (–4 2 5 ) 2 = Power of a product property Power of a power property Simplify and evaluate power. =
Algebra 2-4 Dividing Rational Numbers
Integer Exponents 8.EE.1. Objective - To solve problems involving integer exponents.
1.3 Complex Number System.
Exponent Laws.
Vocabulary, Missing Exponents Negative and Zero Rules
6.1 Properties of Exponents
5.1 Use Properties of Exponents
Evaluate numerical expressions
Example 3 Dividing Mixed Numbers ÷ – 3 19 = 17 6 – Multiply by the reciprocal of 17 6 – 6 – = 3 () 6 – 19 Use rule for multiplying fractions.
Algebra Roots and Radicals. Radicals (also called roots) are directly related to exponents. Roots and Radicals.
Appendix:A.2 Exponents and radicals. Integer Exponents exponent base.
Exponent Rules Essential Question: How can I simplify and evaluate algebraic equations involving integer exponents?
Evaluate the following: Recall: a logarithm is an exponent. So in each case, we are looking for the exponent of 2 to get a number. In the first example,
Section 9-3a Multiplying and Dividing Rational Expressions.
Dividing Monomials: The Quotient Rule and Integer Exponents.
This is Jeopardy!.
Section 6-1: properties of exponents
Rational Expressions – Product & Quotient PRODUCT STEPS : 1. Factor ( if needed ) 2. Simplify any common factors QUOTIENT STEPS : 1. Change the problem.
Evaluating Algebraic Expressions 4-3 Properties of Exponents California Standards NS2.3 Understand negative whole- number exponents. Multiply and divide.
ALGEBRA – LESSON 93 Quotient of Rational Expressions Be ready to grade the homework!
1 Algebra 2: Section 7.1 Nth Roots and Rational Exponents.
5.6 Solving Quadratic Function By Finding Square Roots 12/14/2012.
SECTION 1.4 EXPONENTS. PRODUCT OF POWERS When you multiply two factors having the same base, keep the common base and add the exponents.
4.1 Properties of Exponents
Algebraic Fractions  Know your rules  Anything raised to the 0 power = 1  Negative exponents can be moved to the opposite and made positive (that is,
Multiplying and Dividing Radicals The product and quotient properties of square roots can be used to multiply and divide radicals, because: and. Example.
Adding and Subtracting Radical Expressions
MULTIPLYING RATIONAL NUMBERS IF THE SIGNS ARE THE SAME, MULTIPLY THEIR ABSOLUTE VALUES AND THE ANSWER IS POSITIVE. (+4)(+5) = (-4)(-5) = (3)(6) = (-10)(-4)
11-3 Multiplying Rational Expressions Algebra 1 Glencoe McGraw-HillLinda Stamper.
Notes Over 2.8 Rules for Dividing Negative Numbers. ( Same as Multiplying ) If there is an even number of negative numbers, then the answer is Positive.
Chapter P Prerequisites: Fundamental Concepts of Algebra 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.3 Radicals and Rational Exponents.
Fricovsky 4.5: Do Now: Simplify. 1.
§ 7.5 Multiplying With More Than One Term and Rationalizing Denominators.
Complex Numbers Essential Question: How do you perform operations on complex numbers? Demonstrated in writing on a summary at the end of the notes.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 8 Rational Exponents, Radicals, and Complex Numbers.
Properties and Rules for Exponents Properties and Rules for Radicals
Monomials Interactive In Algebra County. There are 10 problems to work. Keep track of how many you get correct the first time. If you miss the problem,
Zero power - Any nonzero number raised to the zero power is always one (60 = 1) 4.6 Negative and Zero Exponents 24 = = 1 21 = 2 22 = 4 23 =
Holt Algebra Division Properties of Exponents 7-4 Division Properties of Exponents Holt Algebra 1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson.
Algebra 1 Shelby Ferreira. Group Activity Half a number plus 5 is 11.What is the number? Explain your reasoning and create an equation that represents.
A or of radicals can be simplified using the following rules. 1. Simplify each in the sum. 2. Then, combine radical terms containing the same and. sumdifference.
Graphing Rational Functions Day 3. Graph with 2 Vertical Asymptotes Step 1Factor:
Algebra 1 Warm ups Answers: 1) 15√2 + 2√10 2) 6 + 4√6 3) 15√2 + 20√10.
Bell Quiz. Objectives Multiply and Divide signed numbers. Discuss the properties of real numbers that apply specifically to multiplication. Explain the.
13(4x + 5) 8(14x + 9) 12(22x – 6) 14(2x – 8) Simplify the expression using the distributive property: Evaluate when m = 4, y = 5, a = 2 and b = 7 2m +
7.2 – Rational Exponents The value of the numerator represents the power of the radicand. The value of the denominator represents the index or root of.
Limits – Part 2     Use when a specific value “c” is given to evaluate…
Dividing Real Numbers Simplify each expression. a. 70 ÷ (–5)
Multiplying and Dividing Complex Numbers
Lesson 11.2 Techniques for Evaluating Limits
Review Algebra.
or write out factors in expanded form.
Chapter R Algebra Reference.
Lesson 4.5 Rules of Exponents
The product of 3x5  2x4 is 6x20 6x9 5x20 5x9
You replace it with its simplest name
Evaluating expressions and Properties of operations
7-4 Division Properties of Exponents
Dividing Radical Expressions
Simplify: (3xy4)(-2x2y2) x3y6 xy2 -6x3y6
Presentation transcript:

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate…

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate…

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate…

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate…

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate…

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… Factor and cancel…

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… Substitute x = 1

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… This is the same function but there is no “c” to evaluate so we must use the 2 nd equation. When doing these, you will get an algebraic answer.

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… This is the same function but there is no “c” to evaluate so we must use the 2 nd equation. When doing these, you will get an algebraic answer.

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… This is the same function but there is no “c” to evaluate so we must use the 2 nd equation. When doing these, you will get an algebraic answer.

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… This is the same function but there is no “c” to evaluate so we must use the 2 nd equation. When doing these, you will get an algebraic answer. You know you have done it correctly when you have terms that ALL contain some degree of “h”

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… This is the same function but there is no “c” to evaluate so we must use the 2 nd equation. When doing these, you will get an algebraic answer. You will always factor an “h” out in the numerator …

Limits – Part 2 Use when a specific value “c” is given to evaluate… Use when no specific value “c” is given to evaluate… This is the same function but there is no “c” to evaluate so we must use the 2 nd equation. When doing these, you will get an algebraic answer. Substitute h = 0

Limits – Part 2 When you have a rational exponent involved, some creative Algebra is needed to simplify the quotient…

Limits – Part 2 When you have a rational exponent involved, some creative Algebra is needed to simplify the quotient…

Limits – Part 2 When you have a rational exponent involved, some creative Algebra is needed to simplify the quotient… We will need to rationalize the numerator by multiplying by the conjugate of the numerator…

Limits – Part 2 When you have a rational exponent involved, some creative Algebra is needed to simplify the quotient… We will need to rationalize the numerator by multiplying by the conjugate of the numerator… I used the difference of squares rule for the numerator…

Limits – Part 2 When you have a rational exponent involved, some creative Algebra is needed to simplify the quotient…

Limits – Part 2 When you have a rational exponent involved, some creative Algebra is needed to simplify the quotient…

Limits – Part 2 When you have a rational exponent involved, some creative Algebra is needed to simplify the quotient… Substitute h = 0 and simplify

Limits – Part 2

Distributed negative…

Limits – Part 2 Simplified…

Limits – Part 2 Factored out “h”…

Limits – Part 2 Factored out “h”…

Limits – Part 2