Monthly Archives: نوفمبر 2014

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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2. motion in one dimension

2-1: Position, Velocity, and Speed Position: is the location of the particle with respect to a chosen reference point that we can consider to be the origin of a coordinate system. Displacement: the displacement    of a particle is defined … إقرأ المزيد

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2-7: Freely Falling Object

   In the absence of air resistance, all objects dropped near the Earth’s surface fall toward the Earth with the same constant acceleration under the influence of the Earth’s gravity.    When we use the expression freely falling object, we do … 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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2-6: Analysis Model: Particle Under Constant Acceleration

the particle under constant acceleration. we generate several equations that describe the motion of a particle for this model. or:      (for constant    )  (2.13) Becouse velocity at cnstant acceleration varies linearly in time according to Equation (2.13), … 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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