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UIC / Mathematics / MATH 165 / Explain the use of the function value.

Explain the use of the function value.

Explain the use of the function value.

Description

School: University of Illinois at Chicago
Department: Mathematics
Course: Calculus for Business
Professor: Robert cappetta
Term: Fall 2016
Tags: Calculus
Cost: 50
Name: Math 165
Description: Detailed study guide for the final
Uploaded: 04/29/2017
16 Pages 125 Views 1 Unlocks
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MATH FINALWe also discuss several other topics like What is the definition of human nature?
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1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7,  2.8, 3.1, 3.2, 3.3, 3.5, 4.1, 4.2, 4.3, 4.4, 4.5, 5.1, 5.2 6.1, 6.2, 6.3, 6.5

1.1. Limits: A Numerical and Graphical Approach

  • Definition
  • As x approaches a, the limit of f(x) is L, written
  • “x → a”: This indicates that x is approaching a from both sides
  • Theorem
  • As x approaches a, the limit of f(x) is L if the limit from the left exists and the limit from the right exists and both limits are L that is
  • If,  =  then,
  • Function value and limit are not the same
  • The limit of f(x) at a number a does not depend on the function value at a or whether a exists

1.2. Algebraic Limits and Continuity

  • Theorem Limits of Rational Functions
  • For any rational function f, with a in the domain of f:

                Don't forget about the age old question of What are the 4 classes of connective tissue?
Don't forget about the age old question of The study of the earth is called what?

  • Definition
  • A function f is continuous at x = a if:
  • 1. f(a) exists
  • 2.  exists                (continuous)
  • 3.                 (continuous)
  • Marginal cost is different from average cost
  • DIfference quotient
  •  
  • ;

Don't forget about the age old question of How do people get high levels of market power?

Don't forget about the age old question of In declaratory theory, what do the judges do?

  • Ex. 2. Find Δ y in each case
  • a. y= x 2, x= 4, and Δ x= 0.1
  • Δ y = (4+0.1) 2 - 4 2
  • (4.1)2 - 4 2 = 16.81 - 16 = 0.81
  • b. y= x 3, x=2, and Δ x= -0.1
  • (2-0.1)3 - 23 = -1.141
  • f’(x) =
  •  ; ;

  • Ex. 3
  • y = f(x) =
  • a. Find dy when x= 4 and dx= 1
  • b. Compare dy and 0 Δ y
  • a. use the results of a and b to estimate value of
  • a.
  • b. The value of Δ y is the actual change in y between x= 4 and x= 10.
  • Δ y =
  • c.

1.6. Differentiation Techniques: the Product and Quotient Rule

  • f(x) = u*v
  • f’(x) = u * v’ +u’ * v
  • Quotient rule:
  • Q(x) = ;  

1.7. The Chain Rule

  •   

2.1. Using first derivative to classify maximum and minimum values and sketch graphs

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