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Calculus

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Limits

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Limits Number value that f(x) approaches as the values of x approach a specific numberIf f(x) is a polynomial or a rational function and a is in the domain of f(x), then Limits that fail to exist 1. If f(x) approaches a different number from the right than from the left: 2. If f(x) increases or decreases without bound as it approaches a number: 3. If f(x) oscillates between 2 fixed value One-sided limits If only approaching from the right If only approaching from the left Limit Existence Theorem = L iff = L = Vertical Asymptote If = or = Then x=a is a vertical asymptote Horizontal Asymptote If or Then y=b is a horizontal asymptote

Continuity

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Function continuity at x=a (bridges) F(x) is continuous at x=a if must exist f(a) must be defined f(a)= Ex. Continuous: f(a) is defined f(a)= Ex. Discontinuous: f(a) is defined f(a)
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CliffNotes Calculus AB & BC

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PETERSON?S MASTER AP CALCULUS AB & BC 2nd Edition W. Michael Kelley Mark Wilding, Contributing Author An ARCO Book ARCO is a registered trademark of Peterson?s, and is used herein under license by Peterson?s. About Peterson?s, a Nelnet company Peterson?s (www.petersons.com) is a leading provider of education information and advice, with books and online resources focusing on education search, test preparation, and financial aid. Its Web site offers searchable databases and interactive tools for contacting educational institutions, online practice tests and instruction, and planning tools for securing financial aid. Peterson?s serves 110 million education consumers annually. For more information, contact Peterson?s, 2000 Lenox Drive, Lawrenceville, NJ 08648;

AP CALC AB MIDTERM REVIEW

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AB CALC AP MIDTERM REVIEW SHEET Limits Limit of a constant is a constant 0/? -> 0 Value/0 -> ?? or DNE 0/0 or ?/? Factor Rationalize L?Hospital?s Rule (derivative of numerator? derivative of denominator) End behavior (x->?) look at highest power of numerator and denominator Special Limits: (used in trig limits) Lim(x->0) [sinx/x] =1 Lim(x->0) [(cosx -1)/x] =0 Lim(x->0) [tanx/x] =1 Local Linear Approximation Approximation of a value on a function using a linear function f(x) ? f(xo) + f?(xo) (x - xo) Continuity A function f is continuous at point c if: F(c) is defined Lim(x->c) f(x) exists F(c) = limit Intermediate Vale Theorem

AP CALCULUS BC REVIEW GUIDE

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2009?2010 AP BC Calculus First Semester Exam Review Guide I. ?BIG 7? THEOREMS (be able to state and use theorems especially in justifications) Intermediate Value Theorem Extreme Value Theorem Rolle?s Theorem Mean Value Theorem for Derivatives & Definite Integrals FUNDAMENTAL THEOREM OF CALCULUS ? Be sure you remember the 2nd part is called the Total Change Theorem Also, in your justifications, if a problem says it is differentiable at x = a, then the function is continuous at x = a. (Differentiability implies continuity, but not vice-versa.) II. VOCABULARY/KEY CONCEPTS CHAPTER 1: 1. Distinguish the graphs of parent functions without the use of a calculator. (handout) 2. Define an absolute value function as a piecewise function. (pg. 17)

intro to polar coordinates

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? ( x, y) x y ? ( r, ?) Polar Area Complete each trig identity Discussion of Area
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How to mae good Grades

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HOW TO MAKE GOOD GRADES IN CALCULUS ONE IMPORTANT TIP : DON?T STUDY HARDER STUDY SMARTER
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Calculus Info

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October 24, 2012 October 24, 2012 October 24, 2012 October 24, 2012 October 24, 2012 October 24, 2012 October 24, 2012 October 24, 2012 October 24, 2012
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