Calculus I,    B-Track  
Test #1
September  30, 2002
R.  Hammack
Score ______

(1) (10 points)

(a)  [Graphics:Images/T1BF02sol_gr_1.gif]

(b) Find all the x values that are not in the domain of the function [Graphics:Images/T1BF02sol_gr_3.gif].

(2) (10 points)

(a) Sketch the graph of the equation    [Graphics:Images/T1BF02sol_gr_6.gif].


(b) Find the equation of the line that is parallel to the graph of   [Graphics:Images/T1BF02sol_gr_8.gif] (from Part a, above) and which passes through the point [Graphics:Images/T1BF02sol_gr_9.gif]. Put your final answer in slope-intercept form, and simplify as much as possible.

(3) (10 points)  Consider the functions [Graphics:Images/T1BF02sol_gr_14.gif] and   [Graphics:Images/T1BF02sol_gr_15.gif]

(a) [Graphics:Images/T1BF02sol_gr_16.gif]

(b) [Graphics:Images/T1BF02sol_gr_19.gif]

(4)  (20 points)  Evaluate the following limits.

(a)    [Graphics:Images/T1BF02sol_gr_21.gif]

(b)  [Graphics:Images/T1BF02sol_gr_23.gif]

(c)    [Graphics:Images/T1BF02sol_gr_26.gif]

(d)    [Graphics:Images/T1BF02sol_gr_28.gif]

(5) (35 points) This problem concerns the function  [Graphics:Images/T1BF02sol_gr_33.gif].

(a) State the domain of f.

(b)    [Graphics:Images/T1BF02sol_gr_38.gif]

(c)    [Graphics:Images/T1BF02sol_gr_40.gif]

(d)    [Graphics:Images/T1BF02sol_gr_42.gif]

(e)    [Graphics:Images/T1BF02sol_gr_44.gif]

(f) List the vertical asymptote(s) of f  (if any).  (Feel free to use any relevant information from parts a-d above)

(g) List the horizontal asymptote(s) of f  (if any).   (Feel free to use any relevant information from parts a-d above)

(6) (10 points)  This problem concerns the function [Graphics:Images/T1BF02sol_gr_46.gif]
(a) [Graphics:Images/T1BF02sol_gr_47.gif]

(b) [Graphics:Images/T1BF02sol_gr_49.gif]

(c) [Graphics:Images/T1BF02sol_gr_51.gif]

(d) [Graphics:Images/T1BF02sol_gr_53.gif]

(e) Is f continuous at x = 0? (Explain, using above information.)

(f) [Graphics:Images/T1BF02sol_gr_56.gif]

(g) [Graphics:Images/T1BF02sol_gr_58.gif]

(h) [Graphics:Images/T1BF02sol_gr_60.gif]

(i) [Graphics:Images/T1BF02sol_gr_62.gif]

(j) Is f continuous at x = 1? (Explain, using above information.)

(7) (5 points) Sketch the graph of a function f  satisfying the following properties:  [Graphics:Images/T1BF02sol_gr_64.gif],   [Graphics:Images/T1BF02sol_gr_65.gif],   [Graphics:Images/T1BF02sol_gr_66.gif],  [Graphics:Images/T1BF02sol_gr_67.gif],   and   [Graphics:Images/T1BF02sol_gr_68.gif],  There are many correct answers.