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1 Calculus AB Bible(2nd most important book in the world)(Written and compiled by Doug Graham)PG.Topic24Limits5Continuity56Derivative by Definition78Derivative Formulas910Related Rates 11 Properties of Derivatives 12 Applications of Derivatives1314Optimization Problems1517Integrals/Substitution 17 Properties of Logarithms 18 Newton's method 18 Separating variables 18 Average Value 19 Continuity/Differentiability Problem 19 Rectilinear Motion 20 Mean Value Theorem 20 Studying the graph of fx 21 Trigonometric Identities 21 Growth, Double-Life, and Half-Life formulas 2224Applications of the Integral Area, Volume, and Sums2627Approximating Area Trapezoidal Rule, Left Endpoint, Right Endpoint, and Midpoint 28 1st Fundamental Theorem of Calculus 28 2nd Fundamental Theorem of Calculus 28 Integral as an accumulator 29Finding Derivatives and Integrals given a graph of f (x) 30Integration by Parts
2 LIMITS** When evaluating limits, we are checking around the point that we are approaching, NOT at the point.**Every time we find a limit, we need to check from the left and the right hand side (Only if there is a BREAK at that point).**Breaking Points are points on the graph that are undefined or where the graph is split into pieces. Breaking Points :1)Asymptotes (when the denominator equals 0)2)Radicals (when the radical equals 0)3)Holes (when the numerator and denominator equals 0)4)Piece-wise functions (the # where the graph is split) limxafx right hand limit limxafx left hand limit**If left and right hand limits DISAGREE, then the limit Does Not Exist (DNE) at that point. **If left and right hand limits AGREE, then the limit exists at that point as that value.