© 1987, 1995, 2003 A. Azzolino

- 4. Complete the derivative connect the dots.
- 5.
- Write the equation of the line containing (-2, -5) and (3, 5) in the following forms.

1st: point-slope

2nd: slope-intercept

3rd: general form - 6.
- a.) Graph the set of all points 4 units from the point (3, 5).
- b.) Describe in words this set of points.
- c.) Write two functions to express this set of points.
- 7. Graph the function f(x) = (3x + 13)/(x+4), state the limit of the function in symbols, evaluate the limit of the function as
- a.) x goes to - 4 from above
- b.) x goes to - 4 from below
- c.) x goes to - 4
- d.) x goes to positive infinity
- e.) x goes to negative infinity
- f.) x goes to - 3
- 8.
Graph the function f(x) = (x
^{2}+ 7x + 13)/(x+4), - state the limit of the function in symbols,
- evaluate the limit of the function as
- a.) x goes to - 4 from above
- b.) x goes to - 4 from below
- c.) x goes to - 4
- d.) x goes to positive infinity
- e.) x goes to negative infinity
- f.) x goes to - 3
- 9.
Graph the function f(x) = (- x
^{2}- 7x - 11)/(x+4), - state the limit of the function in symbols,
- evaluate the limit of the function as
- a.) x goes to - 4 from above
- b.) x goes to - 4 from below
- c.) x goes to - 4
- d.) x goes to positive infinity
- e.) x goes to negative infinity
- f.) x goes to - 3
- 10. Show the algebra and calculus required to prove
- (The limit as x approaches 2 of the ratio of the quantity the x squared increased by triple x then decreased by 10 and the quantity of x decreased by two, equals seven).
- 11.Explain in words why the lim
_{x 0}(1/x) doesn't exist? - 12. Is f(x) = 1/(x + 1) ever discontinuous?
- 13. Expand means to multiply as indicated. Expand:
- 1st. (x - 1)
^{2} - 2nd. (x - 1)
^{3} - 3rd. (x - y)
^{3} - 4th. (x - y)
^{4} - 14.The definition of the derivative of f(x), f'(x), begins with the symbol "lim".
- Define f'(x).
- 15.Translate into symbols:
- The derivative of the product of a constant and a function equals the the product of the constant and the derivative of the function.
- 16.Translate into symbols:
- The derivative of the quotient of two functions equals the derivative of the first times the second minus the derivative of the second times the first all divided by the second squared.
- 17. Translate into words:
- If u and v are functions with x as the variable,
- 18.List the steps in computing f'(x) if f(x) = -2(x
^{2}+ 1)^{3}. - 19.Show all work in computing f'(x) = (x
^{2}+ 1)^{2}(3x + 2)^{3}. - 20.The relationship between the slope of the tangent and the slope of the secant as the change in x goes to 0 is depicted in the figure below.
- 1st: Label the figure using your notes taken in class.
- 2nd: State in symbols the relationship involving: limit, slope of the secant, and slope of the tangent.
- 3rd: Explain in words this relationship.
- 21. State in symbols the truths:
- The velocity is the derivative of displacement with respect to time.
- 22. State the relationships which exist between s(t), displacement, v(t), velocity, and a(t), acceleration.
- 23. The set of points describe in question #6 intersects the y-axis in two places.
- a - b.) State the slope of the curve at each of these points.
- c - d.) State the tangent line at each point.
- 24. Explain the First Derivative Test and its use.
- 25. Given this "map" of values of the derivative, f'(x),
- Sketch the graph of f(x) then describe the graph of f(x) for x values from -5 through +10 inclusive.
- 26. In maximizing or minimizing a function over an interval, which values of the function must be computed?
- 27. Your text book, in sections 3.1 and 3.2, contains some very important theorems (laws), definitions, and terms.
- a. Copy into your notebook the contents of each of the boxes of material in these two sections.
- b. During the next test or quiz, show the copied material to the prof to obtain credit for this question.

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