Math 140 - 6381 Quiz #1 Fall 2017 Professor: Dr. John Thomas Name________________________________ Instructions: The quiz is worth 100 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You must show all of your work to receive full credit. You will not receive credit for just an answer, say \"6\". In the rare case for which a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. If you have any questions, please contact me by e-mail (john.thomas@faculty.umuc.edu) At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. ______________________________________________________________________________ I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Your submitted quiz will be accepted only if you have included this statement. Please submit the quiz as an attachment in any readable formats such as scanned or photo copy before or on Sunday, September 3. No late quiz will be accepted. No make-up quiz will be arranged. A solution key for Quiz # 1 will be posted along with the quiz on Monday, September 4. QUIZ # 1 Problems (Please extend sufficient space if you work on the docx version) [15 points] 1. The monthly cost of driving a car depends on the number of miles driven. Juan found that in May it cost him $380 to drive 480 miles and in June it cost him $460 to drive 800 miles. a) Express the monthly cost C as a function of the distance driven d , assuming that a linear relationship gives a suitable model. b) Use part a) to predict the cost of driving 1500 miles per month. c) Draw the graph of the linear function. What does the slope represent? d) What does the y intercept represent? e) Why does a linear function give a suitable model in this situation? [12 points] 2. Use the table to evaluate each expression. x 1 2 3 4 5 6 f ( x) 3 1 4 2 2 5 g( x) 6 3 2 1 2 3 a) f (g ( 1 ) ) b) g( f ( 1 ) ) c) f (f ( 1 )) d) g( g ( 1 )) e) ( g f )( 3 ) f) ( f g )( 6 ) [16 points] 3. For the function g whose graph is given, state the value of each quantity, if it exists. If it does not exist, state why. a) lim g (t ) t 0 b) lim g (t ) t 0 c) lim g (t ) t 0 d) lim g (t ) t 2 e) lim g (t ) t 2 f) lim g (t ) t 2 g) h) g (2) lim g (t ) t 4 [12 points] 4. Evaluate the limit using the limit laws - you do not need to state the laws. a. lim x2 6 x 5 x 5 lim 9 h 3 h x 5 b. h 0 [15 points] 5. Let g ( x) x2 x 6 x2 Find the following: a. lim g ( x) x 2 b. lim g ( x ) x 2 c. Does lim g ( x) x2 exist? [12 points] 6. Consider the function: 3 x 1, if x 1 5, if x 1 2 f ( x ) x 1 , if 1 x 3 x 1 1 , if x 3 x3 a) Sketch the graph of the function b) Determine the numbers for which the function is discontinuous. [12 points] 7. Knowing that: lim ( 2 x5 ) =3 x4 within a) 1 unit of 3? b) 0.6 units of 3? c) 0.09 units of 3? d) units of 3? , what values of x guarantee that f ( x )=2 x5 is