Math 180 #003 UNM Summer 2012
Elements of Calculus I: Worksheet 1
1. Use the graph of below to evaluate parts (a) through (o).
(a) . (b) . (c) .
(d) . (e) . (f) .
(g) . (h) . (i) .
(j) . (k) . (l) .
(m) . (n) . (o) .
2. Use a graph to evaluate the following limits:
(a) . (b) . (c) .
(d) . (e) . (f) .
(g) . (h) . (i) .
3. Use the graph of in the figure in Problem #1 to evaluate parts (a) through (l).
(a) . (b) . (c) .
(d) . (e) . (f) .
(g) . (h) . (i) .
(j) . (k) . (l) .
4. Consider the polynomial function .
(a) Find , , and .
(b) Based on your answer for part (a), factor .
(c) Find .
5. Consider the function .
(a) Sketch the graph of .
(b) Find all the x-values (if any) where is discontinuous.
(c) Find the limit from the left and right of at any x-values found in part (b).
6. The figures below show position versus time graphs for a car. Match each (picture) graph 1-5 with one of the proper (English) descriptions A-G of what the car is doing. (Note: Not all of the choices A-G are used.)
(A) The car is traveling forward at a steady speed.
(B) The car is stopped.
(C) The car is traveling backward at a steady speed.
(D) The car is accelerating and moving forward.
(E) The car is accelerating and moving backward.
(F) The car is decelerating and moving forward.
(G) The car is decelerating and moving backward.
7. In the figure at the right, the straight line is tangent to the graph of at .
(a) Find the y-intercept of the line.
(b) Find .
(c) Find .
8. Use the limit definition to find the derivatives.
(a) . (d) .
(b) . (e) .
(c) . (f) .
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