Assignment:
Q1) Using the following two functions X and X^2 develop their derivatives using the Definition of a Derivative for three values of "h"
h = .1
h = .01
h= .001
and then repeat the calculation
in the limit as h->0
Q2) Using the two functions above, show that the Finite Sum approximation of the area between the two functions approaches the value of the the actual value in the interval 0.5 to 2.5.
Q3) Using Proper Mathish explain the Definition of a Derivative.
Q4) Using Proper Mathish provide a Definition of Integral-- both Indefinite (anti derivative) and Definite Integral.
Q5) Using Proper Mathish, Describe a Finite Sum approximation and how it used
Q6) Describe what a Well-Behaved Function is? and is not?
Q7) Describe in Proper Mathish what a Limit is? and is not?
Q8) Describe what the Fundamental Theorem of Calculus means to you for well-behaved functions?
Q9) Finally, starting with a Finite Sum approximation develop the the relationship between the Lower and Upper Limits of a Definite Integral? Include the effect of changing the width of the rectangles starting with an initial approximation and then "in the limit" case where the width approaches zero.
Provide complete and step by step solution for the question and show calculations and use formulas.