Report

Ch. 6 Review AP Calculus 6.2: Integrals of Reciprocal Functions 6.2: Second Fundamental Theorem of Calculus 6.3: Log Properties (The Big Four) 6.4: Solving Exponential Equations (logs) 6.4: Logarithmic Differentiation (exponential functions) Growth/Decay Problems (using logs to solve)… including Separation of Variables Derivatives/Integrals of Transcendental Functions (trig, exponential, logs) Topics If f(x) = cos 2 , find f’(x). 5 2 1 If g(x) = , find g’(x). Example 8, pg. 276 Second Fundamental Theorem of Calculus 4 8 − 1 3 2 5 − 4 2 tan Integrating Reciprocal Functions 2 4 2 3 log 2 ln 2 Simplifying Logs log 5 +2 7 Derivatives of Logs/ Logarithmic Differentiation Find f’(x) if = (3+7)5 3 +2 Derivatives of Logs/ Logarithmic Differentiation Power Rule, Chain Rule Product Rule, Quotient Rule e^x 5^x ln x log 3 Differentiation/Integration Methods = − + = + sec = ln | sec + tan | + csc = −ln | csc + cot | + tan = ln | sec | + cot = −ln | csc | + Trig Integrals See Population Problem, pg. 269. We now know how to solve this QUICKLY!!! Separation of Variables Know how to substitute given values into R(t) = 0 formula. Be able to recognize derivative (rate of change, instantaneous rate, slope of tangent, etc.) vs. integral (sum, area under curve, total accumulation). Exponential Growth/Decay