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    Rational Expressions‚ Asymptotes‚ and Holes Dr. Litan Kumar Saha Assistant Professor Department of Mathematics University of Dhaka Rational Expression  It is the quotient of two polynomials.  A rational function is a function defined by a rational expression. Examples: y x2 x5 y 3x2  2 x  5 x3  4 x2  5 x  7 Not Rational: y 4x x2 y x x2  5 Find the domain: Graph it: f ( x)  1 x Find the domain: Graph it: f ( x) 

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    © CBSEPracticalSkills.com 1 Edulabz International REAL NUMBERS Exercise 1.1 Q.1. Use Euclid’s division algorithm to find the HCF of: (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution. (i) In 135 and 225‚ 225 is larger integer. Using Euclid’s division algorithm‚ [Where 135 is divisor‚ 90 is remainder] 225 = 135 × 1 + 90 Since‚ remainder 90 ≠ 0 ‚ by applying Eudid’s division algorithm to 135 and 90 ∴ 135 = 90 × 1 + 45 Again since‚ remainder 45 ≠ 0 ‚ by applying

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    Identify the elements of the set of real numbers; and 3. Classify real numbers as counting numbers‚ whole numbers‚ integers‚ rational and irrational numbers II. Reference: E-math K-12 edition by Orlando A. Oronce and Marilyn O. Mendoza p. 12-14. III. Subject Matter Topic: The Set of Real Numbers Material: Diagram of the set of real numbers Vocabulary: integers‚ rational numbers‚ irrational numbers Time Frame: 1 day V. Teaching Strategies A. Connecting to Prior Knowledge Encourage the students

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    1 Quadratic Equations in One Unknown (I) Review Exercise 1 (p. 1.4) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Let’s Discuss Let’s Discuss (p. 1.23) Angel’s method: Using the quadratic formula‚ Ken’s method: Using the quadratic formula‚ Let’s Discuss (p. 1.30) The solution obtained by using the factor method is the exact value of the root. However‚ the solution obtained

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    UC Davis‚ ECS 20‚ Winter 2014 Instructor: Vladimir Filkov Midterm Review Exercises 1. Write the truth table for the proposition (r  q)  (p  r). q Ans: p  q)  (p  r) r (r p T T T T F F F F 2. T T F F T T F F T F T F T F T F T T F T T F F F Find a proposition with three variables p‚ q‚ and r that is true when exactly one of the three variables is true‚ and false otherwise Ans: (p  q  r)  (p  q  r)  (p  q  r). 3

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    Grade 8 Rational Number  Natural numbers are a collection of all positive numbers starting from 1.  Whole numbers are a collection of all natural numbers including 0.  Rational numbers are the numbers that can be written in p form‚ where p and q are q integers and q 0  Closure property 1. Whole numbers are closed under addition and multiplication. However‚ they are not closed under subtraction and division. 2. Integers are also closed under addition and multiplication. However‚ they are

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    Hibernate/JPA‚ HTML/JavaScript‚ JUnit‚ UML‚ XML‚ IBM Rational Application Developer‚ IBM Websphere Server‚ IBM Message Broker‚ Database (Oracle 9i & IBM DB2)‚ HP QC Professional Experience + Cognizant Technology Solutions Associate Kolkata Jan 2011 – April 2014 Led a team of 3 professionals in developing unique middleware software solutions for the Airlines Industry (Travelport Inc.) on Java Platform. Have experience in several IBM tools such as Rational Application Developer‚ Websphere Server‚ Message

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    Governance Approach Business Performance through IT Execution Optimizing business performance through IT strategy‚ goals‚ and objectives Enabling and empowering people to deliver strategic business value Automating IT governance with IBM Rational software Lynn Mueller Matthew Magee Petr Marounek Andrew Phillipson ibm.com/redbooks International Technical Support Organization IBM IT Governance Approach: Business Performance through IT Execution February 2008 SG24-7517-00

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    Addition and Subtraction of Rational Expressions Find the LCD ( Least Common Denominator) Divide the LCD on the denominator and then multiply the quotient on the numerator. Simplify Examples: LCD = 6a LCD = Rational Functions Rational Functions – any function which can be defined by a rational fraction. Domain – makes f(x) defined and real. Examples: Domain: D={x/x ≠ 3} Evaluate the function: and = = or =

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    Amity Campus Uttar Pradesh India 201303 ASSIGNMENTS PROGRAM: BBA SEMESTER-I Subject Name Student Name Roll Number (Reg.No.) Batch : Business mathematics : : : INSTRUCTIONS a) Students are required to submit all three assignment sets. ASSIGNMENT Assignment A Assignment B Assignment C DETAILS Three Subjective Questions Case Study Objective or one line Questions MARKS 10 10 10 b) c) d) e) Total weightage given to these assignments is 30%. OR 30 Marks All

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