Question:

AP Calculus AB Semester 1 Study Guide You should know... 1] 2) 3] 4) 5) 6] 7] 8] 9] 10] 11] 12] 13] 14] 15] 16] 17] 18] 19] 20] 21] 22] 23] 24] 25) 26] 27) 28) 29] 30] 31] 32] 33] 34) 35) 36] 37) 38] 39) 40] 41] 42] 43] 44] 45) The formula for a finding a secant line. The concept of a "limit". How to nd a limit numerically. The 3 conditions that need to be met for a limit to exist. The 4 approaches to problem solving. The 3 conditions where a limit fails to exist. The concept of a "well-behaved" function. The 3 basic types of algebraic functions. At least three techniques for finding limits. The indeterminate form of a function and when it occurs. The three "special" limits. The general concept of the \"squeeze theorem". The 3 conditions that need to be met for continuity. The concept of \"continuous\". The concept of "everywhere continuous". The 3 types of discontinuity. The concept of a "removable discontinuity". The concept of a \"non-removable discontinuity\". The concept of a "one-sided limit". How the greatest integer function works. The concept of an "open interval" [and symbols]. The concept of a "closed interval" (and symbols]. The 5 types of functions which are continuous at every point in their domain. The concept of "The Intermediate Value Theorem\". The concept of a "vertical asymptote". What type of functions can produce vertical asymptotes. How to determine the difference between when a hole exists and a vertical asymptote exists. The concept of limits at innity. The concept of "limits at infinity". The concept of a \"horizontal asymptote\". The 3 test conditions for determining horizontal asymptotes. The symbolic definition of the derivative of a function [you should be able to state it verbatim). Be able to identify the difference quotient part of the derivative of a function. The concept of \"differentiation\". The concept of \"differentiable". The 3 cases where a derivative fails to exist. The 3 primary notations for a derivative. How to use The Constant Rule. How to use The Power Rule. How to use The Constant Multiple Rule. How to use The Sum and Difference Rules. The derivatives of the trigonometric functions. The relationship between the position function, velocity function and the acceleration function. The velocity/acceleration sign chart. How to nd average velocity. 46] 47] 48] 49] 50) 51) 52) 53) 54) 55) 56] 57) 58] 59) 60] 61) 62] 63) 64] 65) 66] 67] 68] 69] 70) 71) 72) 73) 74) 75) 76) 77) 78] 79) 80] 81] 82] 83] 84] How to nd instantaneous velocity. The definition of the exponential function. The definition of e. The basic operations with exponential functions. The definition of the derivative of the exponential function. How to use The Product Rule [don't forget the memory aidl}. How to use The Quotient Rule [don't forget the memory aid!). How to use The Chain Rule (don't forget the memory aidl]. How to use The General Power Rule. The Chain rule versions of the six trigonometric functions. The definition of the natural logarithmic function. The definitions of the logarithmic properties. The definition of the derivative of the natural logarithmic function. The definition of logarithmic function to base a. The definition of derivatives for bases other than a. The definition of a differential equation. The difference between the implicit and explicit forms of an equation. When to use implicit differentiation. How to use implicit differentiation. How to determine if a function has an inverse. How to find the inverse of a function. The guidelines for finding an inverse function. The concept of a "related-rate". The concepts of the extrema "relative maximum" and "relative minimum". How to nd the extrema on a closed interval. The difference between critical numbers and critical points. The concept of "Rolle's theorem". The concept of "The Mean Value theorem\". Two major similarities between Rolle's theorem and the Mean Value theorem. One major difference between Rolle's Theorem and the Mean Value Theorem. The concepts of an \"increasing", \"decreasing", and "constant" function. The concept of a "strictly monotonic" function. How to use the First Derivative Test to classify the extrema of a function. How to use the second derivative to determine concavity. The concept of \"points of inection\". How to use the Second derivative test to classify relative extrema. How to determine the minimums and maximums of a function by looking at the graph of the function's derivative. How to determine the points of inection of a function by looking at the graph of the function's derivative. How to determine the points of inection of a function by looking at the graph of the function's second derivative