by subhan70m
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May 22, 2019

• Chapter 1

• Vertical line test

• Composite functions

• Secant line

• Transformation

• Inverse functions

• One-to-one function

• How to find inverse function

• Chapter 2

• Definition of a limit

• Concept of a limit

• One-sided/Two-sided limits

• Understand and be able to use limit laws

• Squeeze theorem

• Definition of infinite limits

• Limits at infinity

• Continuity

• Theorems of continuity

• Continuity on an interval

• Chapter 3

• Geometric meaning of tangent line and derivatives

• Definition of derivatives

• Relation between differentiable and continuous functions

• Rules of differentiation

• Chain rule

• Implicit differentiation

• Chapter 4

• Absolute maximum and minimum

• Local max and min

• Local extreme point theorem

• Definition of critical points and how to find them

• Test for intervals of increase and decrease

• First derivative test

• Concavity and inflection point

• Test for concavity

• Second derivative test used to identify local max and min

• Be able to solve optimisation problem

• Definition of linear approximation to f at 0

• Mean value theorem

• L\'Hopital\'s rule

• Antiderivative

• Chapter 5

• Geometric meaning of integration

• Regular partition, grid points

• Riermann sum and all variants

• Definite integral

• Net area

• Reversing limit and identical limit

• Be able to use fundamental theorems of calculus to compute definite integral

• Integrals of even and odd functions

• Substitution rule

• Chapter 6

• Area of a region between functions

• Length of a curve

• Chapter 7

• Integration by parts

• Definition of improper integrals

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