SECTION 2.2: PROPERTIES OF LIMITS and …

(Section 2.2: Properties of Limits and Algebraic Functions) 2.2.3 6) The limit of a constant multiple equals the constant multiple of the limit. (“Constant Factors Pop Out.”)

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CHAPTER 1: Functions - kkuniyuk.com

(Section 1.1: Functions) 1.1.4 TIP 1: Think of a function button on a basic calculator such as the x2 or button, which represent squaring and square root functions, respectively. If a function is applied to the input 5, the calculator can never imply, “The outputs are 1 and .” Example 4 (Ages of People) For a relation R, • The set of inputs is the set of all living people.

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SECTION 3.4: DERIVATIVES OF TRIGONOMETRIC …

(Section 3.4: Derivatives of Trigonometric Functions) 3.4.3 We conjecture that gx ()= sinx.If f is the sine function from Part A, then we also believe that fx ()= gx ()= sinx.We will prove these in Parts D and E.

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PRECALCULUS - kkuniyuk.com

(Assumptions and Notation) A.1 ASSUMPTIONS and NOTATION Unless otherwise specified, we assume that: • f, g, and s denote functions. (See Section 1.1.) •• g sometimes denotes Earth’s gravitational constant. •• h may denote a function, or it may denote the “run” in some difference quotients in …

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(Section 2.6: The Squeeze (Sandwich) Theorem) 2.6.3 In Example 2 below, fx() is the product of a sine or cosine expression and a monomial of odd degree. Example 2 (Handling Complications with Signs)

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SECTION 2.5: FINDING ZEROS OF POLYNOMIAL …

2.49 Method 2 We may also use the Synthetic Division process and see if we get a 0 remainder. We do not get a 0 remainder, so 1 is not a zero of fx(). Method 3 Observe from both previous methods that we can

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CHAPTER 3: DERIVATIVES - kkuniyuk.com

(Answers to Exercises for Chapter 3: Derivatives) A.3.1 CHAPTER 3: DERIVATIVES SECTION 3.1: DERIVATIVES, TANGENT LINES, and RATES OF CHANGE 1) a)

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SECTION 1.10: DIFFERENCE QUOTIENTS - kkuniyuk.com

(Section 1.10: Difference Quotients) 1.10.3 The average velocity is 50 mph on 0, 2 in the three scenarios below. It is the slope of the orange secant line.

CHAPTER 7: SYSTEMS AND INEQUALITIES - kkuniyuk.com

(Sections 7.1-7.3: Systems of Equations) 7.06 The figure is helpful, however, in that it seems to confirm that the system has three real solutions (corresponding …

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CALCULUS - kkuniyuk.com

(Front Matter) 0.1 COLOR CODING WARNINGS are in red. TIPS are in purple. TECHNOLOGY USED This work was produced on Macs with Microsoft Word, MathType, Mathematica (for most graphs) and Calculus WIZ, Adobe Acrobat, and Adobe Illustrator.

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1.3 Limits (II) A. Piecewise-defined Functions

1.3 Limits (II) A. Piecewise-defined Functions Let consider that is a piecewise-defined function: f (x) h x x a c x a g x x a f x ( ),, ( ), ( ) 1 Then: lim f …

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