Category Archives: calculus I

2.1: Derivatives and Rates of Change

Tangents 1. Definition: The tangent line to the curve  at the point  is the line through  with slope provided that this limit exists – there is another expression for the slope of a tangent line that is sometimes easier to use. … إقرأ المزيد

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1.functions and limits

1-1 : Four ways to represent function – function f  rule that assigns to each element x in a set D exactly one element, called f(x), in set E. – Usually consider: D,E  sets of real numbers. – Ddomain, and Erange. … إقرأ المزيد

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1-8: Continuity

1. Definition A function  is continuous at a number  if  Notice that Definition 1 implicitly requires three things if  is continuous at  1. is defined (that is,  is in the domain of  ) 2.  exists 3.   2. Definition A function  is … إقرأ المزيد

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1-7. The Precise Definition of a limit

2. Definition Let  be a function on some open interval that contains the number  except possibly at  itself. Then we say that the limit of  as  approaches  is , and we write if for every number  there is a number  such … إقرأ المزيد

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1-6: Calculating Limits Using the Limit Laws

Limit Laws Suppose that  is a constant and the limits and  exist. then 1.  2.  3. 4. 5. if  These five laws can be stated verbally as follows: Sum Law 1. The limit of a sum is the sum of the … إقرأ المزيد

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1-5: The Limit of a Function

 Definition (1): Suppose    is defined when    is near the number    (This means that    is defined on some open interval that contains    , except possibly at    itself.) Then we write and say “the limit of … إقرأ المزيد

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1-3: New functions from old functions

Vertical and Horizontal Shifts: suppose    . To obtain the graph of  shift the graph of    a distance    units upward.  shift the graph of    a distance    units downward  shift the graph of    a distance   … إقرأ المزيد

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1-2 : Mathematical Models: A Catalog of Essential Functions.

A mathematical model is mathematical description of real-world phenomenon, the model is to understand the phenomenon and perhaps to make predictions about future behavior. There are many different types of functions that can be used to model relationships observed in … إقرأ المزيد

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1-1 : Four ways to represent a function

Function – function f  rule that assigns to each element x in a set D exactly one element, called f(x), in set E. – Usually consider: D,E  sets of real numbers. – Ddomain, and Erange. Representations of functions 1- verbally … إقرأ المزيد

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