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Limits (Algebraic) Calculus Fall, 2012
2 What can we do with limits?
5 How can we find limits algebraically? Reduce Conjugate Absolute value tricks
6 How can we find limits algebraically? Reduce!
12 Absolute value! Which “version” of absolute value is appropriate?
13 Absolute value! Using the “negative” version…
14 Absolute value! Using the “positive” version…
15 Absolute value! Using the “positive/negative” version…
ALGEBRAIC EXPRESSIONS Step 1 Write down the question Step 2 Plug in the numbers Step 3 Use PEMDAS Work down, Show all steps.
MULT. INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.
Graph of a Curve Continuity This curve is _____________These curves are _____________ Smoothness This curve is _____________These curves are _____________.
What two numbers will give you a product of 64 and a quotient of 4?
Order of Operations. Warm Up 1) ) 9 x ) ) 20 ÷
CHAPTER 2 Introduction to Integers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2.1Integers and the Number.
ADDING INTEGERS 1. POS. + POS. = POS. 2. NEG. + NEG. = NEG. 3. POS. + NEG. OR NEG. + POS. SUBTRACT TAKE SIGN OF BIGGER ABSOLUTE VALUE.
Graph of a Curve Continuity This curve is continuousThese curves are discontinuous Smoothness This curve is smoothThese curves are not smooth y x y x y.
Many We use many with count nouns How many apples are there? There arent many apples. QUESTIONS AND NEGATIVES.
Addition 1’s to
Addition Facts = = =
Test B, 100 Subtraction Facts
ALGEBRAIC EXPRESSIONS Step 1Write the problem. Step 2Substitute in the values for the unknown (variable). Step 3Use PEMDAS (remember to go left to right).
Copyright © 2011 Pearson, Inc. P.7 Solving Inequalities Algebraically and Graphically.
Multiply/Divide integers Absent 10/14. Example 1 Find the Product 1. 4(-6) 4(6) = 24 Solution How many negative signs does this problem have? there is.
Ex: Solve x 2 + 6x +10 = 0 a = b = c = 1 st 2 nd.
Jeopardy Topic 1Topic Q 1Q 6Q 11Q 16Q 21 Q 2Q 7Q 12Q 17Q 22 Q 3Q 8Q 13Q 18Q 23 Q 4Q 9Q 14Q 19Q 24 Q 5Q 10Q 15Q 20Q 25 Final Jeopardy.
2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt Time Money AdditionSubtraction.
Solving an Absolute Value Equation and Inequality.
8-3 Factoring x 2 + bx + c Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.
Logarithmic Equations Solving Logarithmic Equations.
Copyright © 2002 Pearson Education, Inc. 1. Chapter 2 An Introduction to Functions.
1 Graph Sketching: Asymptotes and Rational Functions OBJECTIVES Find limits involving infinity. Determine the asymptotes of a function’s graph.
Negative Numbers What do you understand by this?.
Combining Functions Sum, Difference, Product, and Quotient Functions.
Solving an Absolute Value Equation. You have already used graphs and mental math to solve some absolute value equations. For instance: 8 and -8This has.
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