calc2_f17_e1_review.pdf - MATH 2242(Dr Ngai Calculus II...

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MATH 2242 (Dr. Ngai) Calculus II Fall 2017 Review for Exam 1 NOTE: The following is only an outline; it is not exhaustive. To thoroughly review for the exam, study materials from lectures, do all practice and homework problems, and study all quiz problems, and related past exam problems. 7.1 (a) One-to-one functions and the Horizontal Line Test (HLT) . Note that we learnt three methods to determine whether a function is one-to-one on an interval I : 1) apply the Horizontal Line Test (HLT) on I ; 2) show that f ( a ) = f ( b ) implies a = b on I ; 3) show that the function is strictly increasing or strictly decreasing on I , (which hold if f 0 ( x ) > 0 or f 0 ( x ) < 0 on I , respectively). (b) Definition of inverse functions. Compositions of inverse functions (i.e., Cancela- tion Equations). (c) Know how to find the inverse of a function. (d) Graphs of inverse functions are symmetric with respect to the line y =?. (e) Know how to find the derivative of the inverse of a function by using the formula ( f - 1 ) 0 ( x ) = 1 f 0 ( f - 1 ( x )) .
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